Topology - Science topic

This relationship has been known since 1937, based on a work by Pavel Alexandrov, however its application and theoretical and practical meaning is apparently not very widespread. Perhaps it is because of the simplicity of these spaces, none of them, except the trivial ones, are no more than T0 spaces. However, the current boom in data AI and other computational methods could make us think about its probable importance (and its relation to Algebraic Topology).

It would be interesting to know, for example, the relations of hypercube with the corresponding finite topological spaces.

Do you have any information on this?

Even with very less wannier spread (nearly 1) band structure deviates a lot from DFT band. Please comment to reduce discrepancy .

A physics experiment [1], driven on an expanding spin-orbit coupled Bose-Einstein condensate, suggested that a self-trapping effect band (explained in terms of the Peierls-Nabarro energy barrier) separates two dispersion domains characterized by a positive mass but a spin reversal. The self-trapping phenomenon was naturally explained by a negative effective mass related to a negative curvature of the underlying dispersion relation (as opposed to parabolic curvatures).

To better contextualise my question from a practical point of view, I will quote Wikipedia ( follow https://en.wikipedia.org/wiki/Spin_(physics) ): “Mathematically, quantum-mechanical spin states are described by ‘vector-like objects’ known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360° does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720° rotation (The Plate trick and Möbius strip give non-quantum analogies).”

I appeal here to physicists in a spirit of free and friendly discussion.

I'm trying to explain organic molecule's adsorption onto activated carbon based on chemical parameters, and I found a good correlation between the adsorption amount and topological polar surface area (TPSA).

However, this parameter is used only to explain pharmaceutical absorption and not for different groups of organic molecules. Instead, electron density has been studied as a very important element in adsorption phenomena.

Can these two parameters be correlative? Does it make sense to consider adsorption and some pesticides TPSA, for example?

Any help would be significant to me.

Thanks.

Which force field is better suited for these complexes?

Computational topology of solitons

The well-established research area of algebraic topology currently goes interdisciplinary with computer science in many directions. The Topological Data Analysis gives new opportunities in visualization for modeling and special mapping. A study on metrics used or simplicial complexes are reliable for future results in the area of mathematics. Today, the machine learning from one side is a tool for the analysis in topology optimization, topological persistence and optimal homology problems, from other side the topological features in machine learning are new area of research, topological layers in neural networks, topological autoencoders, and topological analysis for the evaluation of generative adversarial networks are in general aspects of topology machine learning. On practical point of view, the results in this area are important for solitary-like waves research, biomedical Image analysis, neuroscience, physics and many others. That gives us opportunity to establish and scale up an interdisciplinary team of researchers to apply for funding for fundamental science research in interdisciplinary field.

More Info: https://euraxess.ec.europa.eu/jobs/249043

A problem for all the mathematicians in the world in the areas of Algebraic Topology and Topological Group theory and Automorphism groups of Riemann surfaces and Topological Groups and their Toplogical Genus g.

I am writng a paper in the above areas and one problem has kept me busy for six months now, which I thought of asking you all to see if there is a way to rich the answer I am looking for.

My problem:

Given the equation of a topological Riemann Surface in the following style and form:

F<W>:=GovaField(79);

P<X>:=PolynomialRing(F);

R<Y>:=PolynomialRing(P);

G<Y>:=

FunctionField((X^(13*m)*Y^(13*n) +X^13*n *Y^13*m)+

(X^13*k * Y^13*l +X^13*l *Y^13*k)+

(X^13*p + Y^13*p) -1);

Genus(G):= ?

Question for all Mathematician in these areas:

For what values of the unknown {m, n, k, l, p},

the value of the g = Genus(G):=21763?

For example, if I were to load a .pdb or .cif file to Avogadro or VESTA, is there a way to click on the carbon atoms next to oxygen atoms and label them "Ct" so that then when the coordinate data is exported the new tabulated .pdb has those carbon atoms' coordinate information followed by Ct as the label.

This would be pretty helpful for building molecular topologies in gromacs, amber and the like. I thank you in advance, for your attention.

Hi all,

Please suggest how I need to optimize a small molecule to generate the topology file for the ligand to process it for Protein-Ligand MD simulations.

I have tried to balance the valency of the molecule, after which I have submitted the molecule to CGenff server, but the charge penalty and penalty scores were very high.

After which I have tried to optimize the molecule using Avogadro software. Using the output from Avogadro, I have resubmitted the molecule to CGenff server, after which the penalty score was even higher.

I have also tried PRODRG and ATB but the molecule was broken in case of PRODRG, while processing for MD. The molecule contains 1 chlorine atom, also attaching the warning suggested by ATB server.

Kindly suggest how can I process this molecule? I am really new to this work. Please suggest if I am processing it appropriately or not.

There are numerous Ribe space constructions but ultimately they produce the same general object, a quasi-Banach topology on the direct sum of the real line R with the Banach space l_1 of absolutely summable sequences. In all constructions R and l_1 are algebraic complements but R is closed and not complemented topologically. Every such space is non-locally-convex and Rademacher type 1. However, some embed into Lp for 0<p<1 while others do not. Some versions are minimal which is equivalent to having no basic sequence. Since every subspace of Lp contains a basic sequence, these versions cannot embed into Lp and the versions embedding into Lp must contain a basic sequence. However, every version seems to have the property that the uncomplemented 1-dim. subspace R is a subspace of every inf-dim. closed subspace. Doesn't this mean every version fails to have a basic sequence? Thus, every version is minimal and no version embeds into Lp for any 0<p<1.

Let X be a Banach space with the following properties.

(1) X embeds into every inf. dim. closed subspace.

(2) If T is a vector topology then T is a strictly weaker Hausdorff topology on a subspace

of X if and only if it is the subspace topology of a strictly weaker Hausdorff topology on X.

Question 1: Does (1) follow from (2)?

Question 2: If X is Reflexive, must it be a separable Hilbert space?

Hello everyone!

I'm calculating protein dimer structure in CNS-solve v1.21 using distance restraints obtained from solution NMR experiments.

There is an issue during calculation that most structures (not all) in the ensemble have two specific amino acids: one tyrosine and one phenilalanine broken like shown in the picture. The problem reproduces even after I remove all restraints associated with this amino acids.

I tried to review topology file, but did not find anything suspicious about these residues.

I would greatly appreciate if you could give me any hints on how to solve this problem.

Hi all,

Thanks for taking the time to help me. I have generated a charged oligomer chain using acepype, as it is the only software I have been able to find to automatically parametrize using the OPLS-AA force field. However, the output file indicates that there are atoms that it could not define. I have attached the files for further clarity. Would it be enough to define these groups by hand, assigning them to the functional groups that suit them best in the topology file with this force field?

How is the topology of a closable topological subspace S related to the complement of this subspace in its closure, and of the complement to the S closure the X space?

A subset of a topological space is called delta-open if it is the intersection of

countably many open sets.

D. B. Gauld and others defined a topology on the set X=[0, +infinity[ by

using the sets A\cap [x, +infinity[ , where x is in X and A is a co-finite subset

of X as the basic open sets.

They stated that ever dense, delta-open subset of the space X is of the form

A cap [x, +infinity[ , where x is in X and A is a co-countable subset of X.

However, I have not been able to prove this statement, despite that they

considered it to be obvious. Therefore, I ask you to provide me a

reasonable proof.

Their statement is important. Namely, it can be used to prove that

Volterra spaces are genuine generalizations of Baire spaces.

Relevant references are:

1. D. Gauld et al, On Volterra spaces II, Ann. N. Y. Acad. Sci.

806 (1996), 169--173. ( Example 1.)

2. F. A. Ballone, Volterra Spaces, Dissertation, Youngstown State University,

2010, 74 pp. ( Example 5.3.1.)

If a string vibrates at 256 cycles per seconds then counting 256 cycles is the measure of 1 second. The number is real because it measures time and the number is arbitrary because it does not have to be 1 second that is used.

This establishes that the pitch is a point with the real number topology, right?

I have been seeing and following a lot of work on these topics, it even seems that there are more results on them than on the corresponding classical topics, particularly on general topology.

What could be the cause of such results?

Hello.

I am trying to parametrize a ligand using SwissParam. It generated me topology (.rtf) and parameter (.prm) files, but the topology file isn't working in Autopsf so I can't generate a .psf file for my future NAMD simulation.

Below is the topology file, mol2, and the prm. My assumption is that the ligand has atoms not supported by the CHARMM force field.

i make a design topology of mixer For my graduation project working at 28 Ghz on cadence with UMC pdk and get this result

S(2,1) 3.5db

but when trying to make same topology with another pdk on ADS to make optimization i don't get any good results in addition there is some errors. How can i solve this problems ????

There is no doubt that the current young pure mathematicians question the applicability of many abstract theories enjoyed in pure math courses. It gets worse if an instructor is asked the application of a particular theory he tries to prove in the class that he himself does not know how it applies in real life.

Mathematicians now try much to get to the bottom of this inquiry. One has developed a topology on a nation with aim of making a nation a topological space: and . The question that comes in mind is: is it possible to develop a pure math theory that approximates the physical reality as that of espionage, domination, or alliance in a general topology context using Cantor or Zermelo-Frankael Set theory alone?

The main website is broken and I can't find the topology dataset I want for my experiment.

I wanted to show membrane protein topology in 3-dimensional form with membrane intact. I wanted to show extracellular region, membrane region and intracellular region of protein in 3-d form. I have been using protter but it shows in 2D form only.

I have been running my phylogeny tree in MEGA X. My phylogeny tree doesn't seem to have any major differences between species in plain view, but the branches are becoming more clearly divided and each species looks to have major differences in topological view. What happened to my phylogeny tree?

Hi!

Does anyone know if you can keep the different parts of an assembly separate after running topology optimization on it in Abaqus?

All three parts of my assembly merge to one after I optimize the assemply but I would like to export them separately to 3D print and test the assembly experimentally.

Thanks!!

I have already tried AMBER and other force fields. The problem is with topology file creation. As there is no crystal structure or even a similar structure. So, I have to predict the structure using Ab initio modelling. In AMBER, the H++ server cannot process the model structure. Is there any alternative method for creating a topology file?

Hello

I would like to know : In the context of photovoltaic systems, if it is essential to integrate diodes into modular series and parallel chopper topologies? What is the significance of this integration, and what are the advantages and disadvantages of adding diodes in these configurations?

The diagonal method is built assuming that, if two figure sequences like r = 0.a₁a₂a₃... and t = 0.b₁b₂b₃..., for some n satisfy the inequality aₙ ≠ bₙ, then r ≠ t. However, this is only true under the discrete topology.

Under the standard one, if r = 0.1000... and t = 0.0999..., then r = t although a₁ ≠ b₁.

There is an infinite set of rational numbers in [0, 1], each member of which can be denoted by two different figure sequences.

I am running a RNA ligand simulation on gromacs , i encountered a problem in which the number of coordinates in coordinate file (EM.gro, 2171) does not match topology (topol.top, 30886) file. PLease help me with this problem.

In spite of such effects, the majority of humanity, especially the scientific community – does not learn to bring about a radical re-definition of the pragmatically defined concept of attainable truth. This is the proof of the relevance of a re-formulation of the same by the science of philosophy and by scientific philosophy in the realization and growth of science, technology, etc.

Just within the pragmatic attitude lives and functions a big majority of the humanity. Specifically, the scientific community acts consciously by inhibiting wholesome ideas, actions, and changes in the usually pragmatic functioning of (1) every possible realm of knowledge, including the human project of thinking, feeling, curing, facilitating, etc. or (2) any other realms of life in any given environment and society.

The only given justification has been the urgency (1) to experience “the realizably” theoretical and practical effects of all ideas, actions, and changes as early as possible, (2) to have the awaited “long-term effects” at the earliest, (3) to have it in abundance “in the here-and-now”, etc.

Pragmatism has been the backbone of almost all, most basic and less basic, definitions, practical procedures, etc. in logic, mathematics, physical sciences, biological sciences, human sciences, etc. Pragmatism acquires constantly new definitions in history of science and philosophy.

By ‘pragmatism’ is meant not exactly and not only the philosophical school under this name. Of course, this philosophical school extols the effects-only and use-only theory beyond the emphasis it assigns to theoretical breadths and depths. In general, such emphasis plays an exaggerated role in determining the forms of access to what humanity needs in terms of life and truth. It is mainly the sciences that effectively inhibit any efforts beyond pragmatism.

The suggested new paradigm beyond pragmatism would be: The more the certainty and generality of the theoretical breadths and depths assured by the axiomatic foundations – the greater the truth of the specific, the individual, and the delineated results of such a founded philosophy and science within life and knowing.

I shall explain in other words the pragmatic state of the sciences. After all theoretical and experimental search, truth is being concluded to – albeit for a short time and with some or much assurance of probabilistic tenability – in a manner that is FULLY representative of the state of affairs sought to be represented.

The representation of an objectual process in a truth statement is taken to directly correspond or correspond enough to reality, when the theoretically antecedent instruments are universal enough to produce the knowledge about anything specific. But the antecedents are never universal enough, if the theoretical foundations are not broader than the theoretical grounding available in the positive sciences or formal sciences.

This sort of truth-representation is what knows, feels, cures, and facilitates life today, purportedly “in all respects”. Hence, pragmatism is merely be about the method of approaching truths and activities. But it has not been sufficiently about concluding something from a swarm of structures of theoretical generality and superiority, which should have worked in terms of theoretical and practical applicability in all possible specific cases available in any theory that is trans-pragmatic.

One example where the attitude of more general theoretical justification is missing is in the diverse theoretical constructs in physics. Anyone can characterise one of the many reasons as the blind and pragmatic acceptance, by many physicists, of the velocity of light as sacrosanct everywhere in the cosmos. In fact, we have been able to prove the velocity of light only with respect to our part of the universe, and have accepted it as the highest for all parts of the cosmos solely because we have not been able to detect one of higher value.

This is due to the overemphasis on pragmatism in science. Using such a limit velocity in science for technological success is a necessity, but insisting on it even in the broadest possible theoretical situations is cheap adherence. In this respect, the matter that none can accept is the way in which Einstein’s postulation of c as the reference velocity to measure and calculate other but lower velocities becomes accepted as the final proof of the very postulation!

What else is it but the consequence of strict pragmatism in the method and procedure of inquiry without enough antecedent theoretical broadening in the foundations, method, and procedure? This has debilitated science and philosophy of science for almost a century and a quarter. How to dispense with such pragmatism in science and philosophy?

Additionally, the declaration that the observed source-independence of luminal velocity is somehow a basis for accepting a background ether for luminal velocity to hinge upon, is again another instance of overmuch pragmatism in the method and procedure of theorization without restricting strict pragmatism to drawing conclusions.

A second example of strict pragmatism is the way in which some absolutely spherical geometries and their topologies were and are even now being used to geometrize the universe. They tend even to conclude from such a presupposition that the universe is spatially and temporally isotropic, and then tend to dispense with the effects of the locally causal temporal dimension on the universe.

Yet another example is the blind acceptance of the pragmatically probabilistic interpretation of quantum physics as the essence of all physics and of all physically existent reality, whereby most physicists attempt to accept a merely epistemic sort of causality in physical reality and call it “probabilistic causality”, and then start using it as if it were physical-ontological causality.

What we can understand (probabilistically, epistemically) need not be the same as how nature is out there! What in fact is the probabilistic causality that acts in physical processes with some parts of it being causal and other parts not causal or even acausal? Is not such a concept of causality a silly idea of causation based on epistemic determinism getting converted into ontological determinism, which then is converted into the actual nature of existent processes? The unnecessarily pragmatic ways of fixing scientific practices is the main reason behind it.

In preparing a short introduction to the following critical presentation of the aftermaths of pragmatism, let me put in gist the new paradigm that is necessitated here: (1) Truth is not merely a subject-object act. (2) Truth is not merely an act of tending towards. (3) Truth is much more an act of epochal finalizing of constant insertion of foundational breadths and depths in the state of affair / process being inquired into, based on the most universal of all conceptual foundations and driving them down onto the particular, but based fully and always on the foundations of the total in a mutually related context.

That is, strict pragmatism should be exercised only at the instance of concluding to the final, strictly contextual, statement and action, and that too under the provision of further constant inquiry and enhancement of the descriptions, conclusions, etc.

My contention concerning strict methodological pragmatism is that, although the pragmatic attitude has its rights over thought and practice, it (1) inevitably foregoes many fundamental (most broadly based on the totality of all existents) aspects of reality, environment, and life and, (2) in consequence, unbridles back onto the same reality, environment, and life the epistemically guided ontological aftermaths of the negligence of the said fundamental theoretical aspects and necessities of reality and of knowledge – and consequently of course onto life and the human ideal of comprehension of reality and life.

Hence, it is high time that philosophy and science eliminate as much as possible the defective, strictly pragmatic attitude from their foundations while safeguarding some of the necessary aspects of pragmatism merely when they create advantages via accessing conclusions and actions, without causing philosophical, scientific, and human-life tragedies.

As there are countless disadvantageous aftermaths of pragmatism in knowledge and life, some of them may be cited in the following:

(1) International, national, and local politics purposefully manipulating natural resources, economies, societies, religions, and nations for power and wealth, even to the extent of impoverishing the majority of a continent or nation.

(2) National and international poverty alleviation programs and techniques which increase the rich-to-poor differences by perpetuating pragmatically charitable corruption in industrial, educational, health, and governmental ventures.

(3) Educational systems and methods becoming partially aimed at creating a vast majority of cheap labourers for the industry especially in poor nations, by fast-paced and obscurantist information-encrypting of sciences, humanities, and languages in educational institutions, without reference to the history of future-oriented achievements in discoveries, ideas, theories, events, programs, etc.

(4) Most media entities creating sensational partial truths as the short-time highest truths at the behest of politicians, industry, research & development, or at least against them, meant finally for easy financial gains and thereafter for practising political and scientific amnesia at the same truths.

(5) The pharma and health industry adopting and justifying as sacrosanct the mechanist-causalist manners of producing medicaments and treating patients – encouraged mainly by the successes of naturally necessitated urgency in such interventions – and producing chemical medicines so non-holistically (i.e., in ways that do not involve material interactions more minute and life-based than in chemical interactions) that the methods of production and treatment necessarily have more than intended side-effects creating ever more patients.

(6) Industries, technological companies, media entities, media producers, and a few nations specializing in hyperbolically creating and satisfying unhealthy and unessential psychological and physical needs and increasing easy production of commodities for quick-growth in economy, resulting in universal pollution of genes and life-forms.

(7) Constitutions of nations and justice-dispensation systems formulated in ways that normally foster or at least merely facilitate the exigencies of the powerful and rich and possibly get favoured in return.

(8) Governmental law-enforcement arms which work on old-fashioned and corruption-facilitating machinery and, from time to time, can milk the rich and powerful by way of protection of their pragmatic socio-economic attitudes.

(9) The more than two centuries of spread of chemical fertilizing methods of agriculture by blocking the spread of great natural cultivation methods and researches into them, callously titling the latter “unscientific”, and thereby chemically cluttering the whole cultivable and life-worthy earth.

(10) The millennia-old mammoth culinary science and eating culture that encourage tasty junk consumption at home and outside, successfully encouraging and perpetuating the enjoyment of quick pleasure from the one end of the tongue to the other.

(11) The way in which human beings, for millennia, exhaust and emaciate themselves in pursuit of quick joys, vastly unaware of the merely brain-based connotative nature of quick joys.

(12) The methods of finance acquisition and offspring-maintenance in families, societies, nations, and religions, oriented at self-perpetuation and attaining – for that same reason – nothing of it.

(13) Eco-compatibility efforts all over the nations by governments themselves, that help further industrialize under cover of grand holistic statements and schemes.

(14) Economic, educational, cultural, health, and other diverse forms of solution of problems of humanity, in which policy makers never go for the deepest roots of maladies: e.g., the real reason why people build houses on and cultivate (e.g., occupying and cultivating steep hill-sides, thus inundating the high ranges), is not merely craving, but the high rate of population growth, and yet no government acts in this direction ethically and democratically via education.

(15) The manner in which the very oppressed groups become much like the oppressor groups and indulge in pragmatic tactics against their own status, and consume the effects of such self-poisoning.

(16) The universal ignominy to what the experiences and the universal phenomenon of rational reflections of the old and dying are – including those of former scientists, technocrats, and scholars.

(17) The wide-spread technocratic and allopathic health-scientific methods of nipping all nature-infused living methods by blanket-terming them as unscientific.

(18) Religions’ millennia-old and continuing promise of a quick and miraculous transfer to a body-less state similar to that of a supposedly vacuous Absolute, instead of the more possible and reasonable “continued growth” of love-bodies as fully well caused by the same kind of growth during the lifetime of individuals and societies in imitation of an infinitely active love-bodied Source.

(19) A section of scientists and philosophers wilfully presupposing that anthropomorphized expressions and theologies based on them are the meaning of religion and spirituality, and basing their science, technology, medicine, and philosophy, etc. on notions that counteract these vicious concepts that should not have been the meaning of religion and spirituality.

(20) Some or many of those involved pragmatically in the above thought patterns and sciences trade their guns against supposed realities that do not exist in the sciences and in the world out there, thus beating in the air to kill some form of ideas that do not exist where they think them to exist.

The most suitable examples today in theoretical sciences are Russell, Wittgenstein, and many others in the early half of the 20thcentury, and Stephen Hawking, Richard Dawkins, Lawrence Krauss, and a host of others in the latter half of the 20th century and thereafter. The ways in which the likes of these experts have unquestioningly been using the already existing pragmatism in physics, cosmology, and philosophy is symbolic and emblematic of pragmatism as a cut-throat methodology in effect.

Technological examples are the ways in which Newton’s physics and mechanistic chemistry, biology, economics, etc. are being used today to facilitate money-flow into the industry by disregarding their health-related and environmental aftermaths.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Can somebody tell me how we worked with a topology-based routing protocol to alter it and under what limitations we did additional study in simulation?

While performing Protein-Ligand interaction in Gromacs version 2021 using the command line: gmx grompp -f ions.mdp -c solv.gro -p topol.top -o ions.tpr. I encountered this Fatal error: number of coordinates in coordinate file (solv.gro, 29336) does not match topology (topol.top, 54674).

I want to know how can I solve and correct this mismatch?

I am attaching both the files of topology (topol.top) and solv.gro

Thanks

I tried to set .itp section after charmm.itp section but did not work

Two-dimensional Skyrmion topology can be quantized to form a quantum superposition of baryons and vibrational resonance states. (Wong, Stephen [2002]. "What exactly is a Skyrmion?". arXiv:hep-ph/0202250) This is quantum entanglement which is inextricably linked to topology. The fact that the topology only exists as a combined entity of the two photons suggests it could possibly combine not merely 2 photons but every photon in space-time (space AND time). George Yuri Rainich's 1925 paper pointed out similarities between gravitation and electromagnetism. So all the photons might be united with all the gravitons in spacetime.

Suppose we accept Albert Einstein's 1919 paper asking if gravitation (and electromagnetism) play a role in forming elementary particles. This paper is often regarded as outdated by discovery of the nuclear forces but my Opinions article in the journal "IPI Letters" says gravitational-electromagnetic interaction can produce the masses and quantum spins of the nuclear-force bosons, as well as of the Higgs boson. Accepting Einstein's 1919 paper means all mass in spacetime might combine with the united photons and gravitons - resulting in quantum gravity? And perhaps the two-dimensional topology can be identified with the Mobius strip in the way my article in IPI Letters details.

Is there a connection between fixed point theory and algebric topology

I am trying to create the topology of a Metalloprotein that contains copper as an essential cofactor. However, it is giving errors, in crystals and modeled structures. I'm very new to the DM field and I'm trying to learn it myself. Can someone help me? Below is the link with PDB of a my protein, and a crystal (other protein) which is already adequate for copper loads

Here by "surface" I mean a projective variety of dimension 2 (over an algebraically closed field k, as in Ch.1 of Hartshorne).

My question is:

Given a positive integer n >0, can we define a (possibly singular) surface S in n-dimensional projective space P^n, such that S does not admit an embedding into any P^m for m < n ?

That is, I am asking for a constructive proof, an effective algorithm taking as input n, that generates the set of homogenous polynomials defining such a surface.

How does this relate to the number and degrees of the homogenous polynomials required to define S ?

There are several known contributions of Topology to ML.

But: what has been the contributions of ML to the research on General Topology, and particularly to Finite Topological Spaces? Do you have any information of this regard?

I am working on molecular docking and dynamic simulation of protein-ligand complex, and the complex generated MD.xtc file of 4.3 gb which I am unable to open in UCSF Chimera through MD movie option. I know that limited RAM of my system is creating this issue, but is there any other way to do it.

I also found that spliting trajectory file helps, but I am getting the following error (Screenshot 2023-11-27 13-31-13.png) while entering MD.tpr and MD.xtc in MD movie Gromacs option. Which I know is because the topology file is not splited like the trajectory file. So, how to rectify this issue, if there's no other way to work around.?

I am using Ubuntu OS, with 8gb ram, 2gb graphics 1650.

Q=1: How can plot 3D graphs for topological indices by using Mathematica software??

Request:

Plz send any coding for 3D mash graph related to attached sample graphs.

I would like to perform a shape optimization on a topology optimized component without exporting and importing the part as .stl, since in that way I loose all the properties, the loads and the BC. Please, is there any chance to to this?

I've been wondering because the definition of an eta-open set is if A ⊆ int(cl(int(A))) U cl(int(A)). While the semi-open set is if A ⊆ cl(int(A)). So, if int(cl(int(A))) just a subset of cl(int(A)), then int(cl(int(A))) U cl(int(A)) = cl(int(A)). This implies that an eta-open set is equivalent to a semi-open set. Can anyone enlighten me with this? because I've looking for examples that make these two sets not equivalent and still nothing found yet.

F(X,Y)= set of all functions from a topological space X to other space Y.

C(X,Y)= set of all continuous functions from a topological space X to other space Y

Compact open and compact convergence topology are comparable, if Yes then which one is finer on F(X,Y) (not on C(X,Y))

Will it be a Majorana mode? But, Majorana modes are typically characterized by their strong localization at one end. If an edge mode is not strongly localized at one end and extends significantly along the other edge, could be an ordinary edge state or a different type of topological mode?

I am working on topology optimization using the parametric level set method. Regardless of the methodology, I thought it might be a generic problem in Topology optimization with which many researchers in the field have faced. The problem is that I cannot achieve smooth boundaries even though I am using the level-set method to produce smooth boundaries. I am using two different grids and meshes for the mechanical and the level-set domains. I thought I needed to increase the number of Finite elements from 350 to 1000, but nothing changed, you can see it from the bottom right figure. Nor did increasing the number of grid cells in the level set domain improve my result.

Thank you in advance for your help.

Best regards,

Farzad

Are the oil-water partition efficient (logP) and Topological polar surface area (TPSA) of energetic compounds related to their molecular stability? How do these parameters relate to the molecular structure?

Generally, a topology tau on a set X is defined considering the following three axioms:

1. The whole set X and empty sets are in topology tau.

2. Arbitrary union of any collection of open sets of tau is in tau.

3. Finite intersection of any collection of open sets of tau is in tau.

Is it possible to construct a topology tau on X without considering first axiom?

To study the topology of the MOF crystals

I am writing to seek assistance on a matter related to n2t file generation. I am using GROMACS and charmm36 force field in my work. I am covalently attaching a short polymer(poly-peptide) to a nanosheet with the carbonyl carbon of the polymer attached to the nitrogen of the nanosheet I obtained the parameter(itp file) for the polypeptide from CGENFF then added the corresponding atom types and charges from the itp to my n2t file the monomer of the poly-peptide is histidine and it’s itp file has various hydrogen atom type along with carbon types with different charges I have added them all in the n2t file in the same sequence as in the itp since most these atom types are attached to carbon when topology is created using x2top wrong type of carbon and consequently wrong charge is assigned to the atom of my structure. I want you to note the hydrogen types as well as the nitrogen type NG2R51 in the topology file at line 134 it is supposed to be a NG2S1 nitrogen type with a -0.555 charge. There are many other atoms whose atom type was supposed to be different. How can I obtain correct topology.I am attaching the itp file(plh.itp) along with the ss of topology and n2t file. Any guidance or pointers would be of immense help. Thank you for your time.

Are there any publications on the topological properties of nonstoichiometry loci - in general and, in particular, in intermetallic compounds?

Let (X, tau, I) be an ideal topology I ask:

wThe product of this topology itself is ideal topology or not?

Hi.

I am trying to create ligand topology and parameter files using SwissParam webserver. I followed all the steps to create the .mol2 file available in SwissParam page: https://www.swissparam.ch/SwissParam_mol2_file.html.

But this error keeps on coming:

Unfortunately, topology and parameters were not successfully generated for LIG.mol2. A failure report can be found below. Failure report: Possible problem with molecular topology in LIG.mol2. SwissParam will try to reconstruct the topology from coordinates only. Topology and parameters were NOT generated. Please check the validity of your molecule. - Are all hydrogens present in the mol2 file? - Is the mol2 file correct? Please, read "How to obtain a correct mol2 file?" in the www.swissparam.ch website.

For reference, I am providing my ligand.mol2 file and lig_fix.mol2 which I have created for performing protein-ligand simulation using Gromacs and CHarmm27 forcefield.

Please help me solve this query.

Thank you for consideration.

Alvea Tasneem

I have been using PRODRG for small molecules topology for years, but now I can't access it, I have emailed its developers but couldn't get any response. I want to use Gromacs forcefield, so I have only 2 options, one is ATB which is not free for new molecules, and another one was PRODRG. Kindly give me suggestions if you know any other way. I have tried Swissparam and switched to Charmm ff but it also didn't work and gave me errors with LJ and at the energy minimization step.

I am starting a new area of research that is Algebraic topology. Kindly suggest some latest problems and related publications

I am having an issue regarding Phosphatidic acid topology generation for Gromacs 5.1.5 simulation. I would like to study the protein-ligand dynamics. Kindly help

After running this step to create ligand topology for molecular dynamic simulation protein-ligand complex:

It showed some tracebacks and import error:

I tried to generate charmm36 topology and parameter files for copper ions on laccase enzyme but it presents an error that says "No residue in CHARMM forcefield". So I've tried CSML Search to parameterize ligand FF using PDB coordinates but the erros persists.

I am new to amber any trying to use xleap to make a tetrapeptide tuftsin. After solvation with TIP3PBox 14.0 iso, when I try to save the inpcrd and prmtop file using command

saveamberparm foo tuftsin.inpcrd tuftsin.prmtop

it gives following message

Checking Unit.

WARNING: There is a bond of 3.610664 angstroms between:

------- .R<WAT 886>.A<H1 2> and .R<WAT 886>.A<O 1>

WARNING: There is a bond of 4.162462 angstroms between:

------- .R<WAT 886>.A<H2 3> and .R<WAT 886>.A<H1 2>

WARNING: The unperturbed charge of the unit: 2.000000 is not zero.

-- ignoring the warnings.

Building topology.

Building atom parameters.

Building bond parameters.

Building angle parameters.

Building proper torsion parameters.

Building improper torsion parameters.

total 11 improper torsions applied

Building H-Bond parameters.

Incorporating Non-Bonded adjustments.

Not Marking per-residue atom chain types.

Marking per-residue atom chain types.

(Residues lacking connect0/connect1 -

these don't have chain types marked:

res total affected

CARG 1

I am not getting how to solve this error message.

I want to simulate a grid-road topology (organized streets) with vehicles generate traffic to Road Side Unit (RSUs). Also, if I need to ramp up quickly to 100 or 200 vehicles how can I do that?

I am seeking a pdf or doc file . #Molecular_Dynamic_Simulation #Gromacs #Protein-Protein MDS Hey, I am working on a project where MD simulation is needed for protein-protein interaction in a dynamic nature. I have previous experience of doing protein-ligand MD simulation from Lemkul's tutorial. Now I am facing a few problems, including 1. In the protein-ligand case, first build the protein topology and then the ligand's one. In the ligand topology generation section—another server used to obtain itp files and introduce them to the protein topology file— In protein-protein MDS, what should we do? Where we get the topology of another protein.

12

If we want to calculate several M-polynomials which method is the most suitable.

I ran gromacs with command: grompp -f ions.mdp -c protein a_solv.gro -p topol.top -o ions.tpr. and yielded a Fatal error:

number of coordinates in coordinate file (solv.gro, 57741)

does not match topology (topol.top, 57742)

how to correct the match of protein a.gro and topol.top file?

While I was trying to generate ligand topology using CGENFF, the penalty score exceeded 50 (parameter penalty 141; charge penalty= 56.475). how do I reparameterize to obtain acceptable penalty score range?

The fixed point property is a fundamental concept in topology and has been extensively studied in various contexts. However, there are still several open problems related to the fixed point property. There are many other interesting questions and directions of research in this area.

I am trying to find out the topological hall effect for my system of study. I currently have no idea about the process and what software packages to use. I know that we can find the anomalous hall effect (AHE) using the Wannier90 package. Any suggestions regarding this will be greatly appreciated.

I want to perform MD simulation on a protein that contains water molecules in PDB what forcefield parameters (topology/ parameter ) files should one use ?

Hello everyone,

While performing MD simulations of protein - ligand complex, at the adding ions stage I am facing an error :

Fatal error:

Syntax error - File UNK_fix.itp, line 7

Last line read:

'[ atomtypes ] '

Invalid order for directive atomtypes

Well, since I've used Swissparam to write the topology file of the ligand (UNK_fix.gro) which usually uses CHARMM all atom forcefield and the protein topology I've written with the charmm36-2019.ff. Can this be a reason that I'm facing the above error?

I've also referred to other options like #include statements which I suppose are correct and the editing in topology is all done right. For reference:

; Include Position restraint file

#ifdef POSRES

#include "posre.itp"

#endif

; Include ligand topology

#include "UNK_fix.itp"

; Include water topology

#include "./charmm36-mar2019.ff/tip3p.itp"

#ifdef POSRES_WATER

; Position restraint for each water oxygen

[ position_restraints ]

; i funct fcx fcy fcz

1 1 1000 1000 1000

#endif

; Include topology for ions

#include "./charmm36-mar2019.ff/ions.itp"

[ system ]

; Name

Protein in water

[ molecules ]

; Compound #mols

Protein 1

UNK 1

SOL 24553

So, please guide me through any other suggestions which may correct this error.

Thank you in advance!

I want to use cpptraj for some analysis but I need to convert my topology and trajectory files from Gromacs xtc, tpr format to Amber nc and parm formats. Could you please let me know how can I convert topology and trajectory files from Gromacs to Amber?

How to prepare topology file for coordination (complex) compounds. Topology files for organic ligand molecules can be obtained using online servers such as SwissParam and etc. How to prepare a topology file for a metal-containing ligand?

gmx grompp -f ions.mdp -c solv.gro -p topol.top -o ions.tpr

Fatal error: number of coordinates in coordinate file (solv.gro, 198459)             does not match topology (topol.top, 198458)

Hi everyone,

I'm trying to optimize a very simple steel element (see figure) with a cyclic load applied in the two red regions. The settings are the standard ones (minimize strain energy, final volume 30%) However, after 6 cycles, the optimization process plot shows a flat curve and the result confirms that something has gone wrong. How can I solve the problem?

many thanks in advance

In fact, the phase will affect the amplitude distribution. For example, the OAM phase will cause the amplitude center to produce a small circle with an intensity of 0, and it will become larger as the topological value of the phase increases.