arXiv subjects

Niladri Patra

Publications and source records attributed to Niladri Patra.

7 recordsLinked to original sources

arXiv2026

Compressive Domains and a Bound for the Number of Components of the Fixed Locus of a Self-Map of the Berkovich Line

We introduce the notion of a "compressive domain" for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. We prove that such a domain always contains a classical fixed point, and we leverage this fact to give a sharp upper bound for the number of connected components of the fixed locus of a rational function. We give a second proof for polynomial functions that uses a previously unpublished mass formula of Rivera-Letelier. Finally, we give an explicit formula for the crucial weight inside a compressive domain as a function of the number of classical fixed points and boundary points.

math.AG↗

arXiv2026

Structure of the Components of the Fixed Locus of a Self-Map of the Berkovich Line

We describe the local and global structure of the fixed locus for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. This includes a bound for the number of connected components that is sharp when the residue characteristic is large or zero. The case of small nonzero residue characteristic will be treated in a subsequent article.

math.AG↗

arXiv2025

Connected components of Berkovich fixed locus: Potential good reduction

Let $\mathbbm{P}^{1,an}$ be the Berkovich projective line over a complete, algebraically closed, non-Archimedean field. Let $\phi$ be a degree $\geq 2$ rational map with potential good reduction, acting on $\mathbbm{P}^{1,an}$. In this article, we study the topology of the fixed locus of $\phi$. we show that the reduction of $\phi$ at its type~II totally ramified fixed point dictates the topological structure of the fixed locus of $\phi$. We give an easily verifiable equivalent criterion for the fixed locus of $\phi$ to be connected as well as an equivalent criterion for the fixed locus of $\phi$ to be finite. Moreover, we provide a sharp upper bound for the number of connected components of the fixed locus of a rational map with potential good reduction.

math.DS↗

arXiv2025

Revolutionising Antibacterial Warfare: Machine Learning and Molecular Dynamics Unveiling Potential Gram-Negative Bacteria Inhibitors

Diseases caused by bacteria have been a threat to human civilisation for centuries. Despite the availability of numerous antibacterial drugs today, bacterial diseases continue to pose life-threatening challenges. The credit for this goes to Gram-Negative bacteria, which have developed multi-drug resistant properties towards \b{eta}-lactams, chloramphenicols, fluoroquinolones, tetracyclines, carbapenems, and macrolide antibiotics. V arious mechanisms of bacterial defence contribute to drug resistance, with Multi-Drug Efflux Pumps and Enzymatic degradation being the major ones. An effective approach to cope with this resistance is to target and inhibit the activity of efflux pumps and esterases. Even though various Efflux Pump Inhibitors and Esterase resistant macrolide drugs have been proposed in the literature, none of them has achieved FDA approval due to several side effects. This research has provided valuable insights into the mechanism of drug resistance by RND efflux pump and Erythromycin esterase. A handful of potential efflux pump inhibitors have been predicted through machine learning and molecular dynamics.

physics.comp-ph↗

arXiv2023

Irreducibility of eventually $2$-periodic curves in the moduli space of cubic polynomials

Consider the moduli space, $\mathcal{M}_{3},$ of cubic polynomials over $\mathbb{C}$, with a marked critical point. Let $\mathscr{S}_{k,n}$ be the set of all points in $\mathcal{M}_{3}$ for which the marked critical point is strictly $(k,n)$-preperiodic. Milnor conjectured that the affine algebraic curves $\mathscr{S}_{k,n}$ are irreducible, for all $k \geq 0, n>0$. In this article, we show the irreducibility of eventually $2$-periodic curves, i.e. $\mathscr{S}_{k,2},\; k\geq 0$ curves. We also note that the curves, $\mathscr{S}_{k,2},\; k\geq 0$, exhibit a possible splitting-merging phenomenon that has not been observed in earlier studies of $\mathscr{S}_{k,n}$ curves. Finally, using the irreducibility of $\mathscr{S}_{k,2}$ curves, we give a new and short proof of Galois conjugacy of unicritical points lying on $\mathscr{S}_{k,2}$, for even natural number $k$.

math.DS↗

arXiv2023

On irreducibility of prefixed algebraic sets in moduli spaces of prime degree polynomials

Consider the moduli space, $\mathcal{M}_{d}$, of degree $d \geq 2$ polynomials over $\mathbb{C}$, with a marked critical point. Given $k \geq 0,\; p$ an odd prime, we show that the set $\Sigma_{k,1,p}$ of conjugacy classes of degree $p$ polynomials, for which the marked critical point is strictly $(k,1)$-preperiodic, is an irreducible quasi-affine algebraic set. Irreducibility of these sets was conjectured by Milnor, and has been proved for $p=3$ by Buff, Epstein and Koch. We prove that the subspaces of $\Sigma_{k,1,p}$, that arise by varying the ramification index of the marked critical point all the way up to the unicritical case, are all irreducible subvarieties. Finally, using the irreducibility of $\Sigma_{k,1,p}$ we give a new and short proof of the fact that the set of all unicritical points of $\Sigma_{k,1,p}$ form one Galois orbit under the action of absolute Galois group of $\mathbb{Q}$.

math.DS↗

arXiv2017

Layer-by-layer assembly of patchy particles as a route to non-trivial structures

We propose a new strategy for robust high-quality self-assembly of non-trivial periodic structures out of patchy particles, and investigate it with Brownian Dynamics (BD) simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, that can be implemented through differential functionalization of patched and shell regions with specific DNA strands. The other key element of our approach is the use of layer-by-layer protocol that allows to avoid a formations of undesired random aggregates. As an example, we design and self-assemble in silico a version of a Double Diamond (DD) lattice in which four particle types are arranged into BCC crystal made of four FCC sub-lattices. The lattice can be further converted to Cubic Diamond (CD) by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions and the layer-by-layer protocol, a high-quality robust self-assembly can be achieved.

cond-mat.soft↗