Search

This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for any $\mathrm{GL}_n(\mathbb{R})$-distinguished generic representation, we demonstrate that the period does not vanish on the distinguished minimal $K$-type. Furthermore, we establish the triviality of the $\varepsilon$-factor for distinguished representations and offer some applications to the branching problem using theta correspondence., Comment: Comments are welcomed!

We study the computational power that oblivious robots operating in the plane have under sequential schedulers. We show that this power is much stronger than the obvious capacity these schedulers offer of breaking symmetry, and thus to create a leader. In fact, we prove that, under any sequential scheduler, the robots are capable of solving problems that are unsolvable even with a leader under the fully synchronous scheduler FSYNC. More precisely, we consider the class of pattern formation problems, and focus on the most general problem in this class, Universal Pattern Formation (UPF), which requires the robots to form every pattern given in input, starting from any initial configurations (where some robots may occupy the same point). We first show that UPF is unsolvable under FSYNC, even if the robots are endowed with additional strong capabilities (multiplicity detection, rigid movement, agreement on coordinate systems, presence of a unique leader). On the other hand, we prove that, except for point formation (Gathering), UPF is solvable under any sequential scheduler without any additional assumptions. We then turn our attention to the Gathering problem, and prove that weak multiplicity detection is necessary and sufficient for solvability under sequential schedulers. The obtained results show that the computational power of the robots under FSYNC (where Gathering is solvable without any multiplicity detection) and that under sequential schedulers are orthogonal.

Glucose monitoring plays a critical role in managing diabetes, one of the most prevalent diseases globally. The development of fast-responsive, cost-effective, and biocompatible glucose sensors is essential for improving patient care. In this study, a comparative analysis is conducted between pristine and Co-doped hematite samples, synthesized via the hydrothermal method, to evaluate their structural, morphological, and optical properties. The glucose sensing performance of both samples is assessed using a fiber-optic evanescent wave (FOEW) setup. While the sensitivity remains comparable for both pristine and Co-doped hematite, a reduction in the Limit of Detection (LoD) is observed in the Co-doped sample, suggesting enhanced interactions with glucose molecules at the surface. To gain further insights into the glucose adsorption mechanisms, Density Functional Theory (DFT) calculations are performed, revealing key details regarding charge transfer, electronic delocalization, and glucose binding on the hematite surfaces. These findings highlight the potential of Co-doped hematite for advanced glucose sensing applications, offering a valuable synergy between experimental and theoretical approaches for further exploration in biosensing technologies.

In this paper, we consider the mixed tensor space of a $G$-graded vector space where $G$ is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators obtained by Berele., Comment: 16 pages

Iron chalcogenides superconductors, such as Fe(Te,Se) have recently garnered significant attention due to their simple crystal structure with a relatively easy synthesis process, high-temperature superconductivity, intrinsic topological band structure, and an unconventional pairing of superconductivity with ferromagnetism. Here, we report the complex in-plane refractive index measurement of nanometer-thin Fe(Te,Se) flake exfoliated from a single crystal FeTe$_{\text{0.6}}$Se$_{\text{0.4}}$ for photon wavelengths from 450 to 1100 nm over a temperature range from 4 K to 295 K. The results were obtained by employing a two-Drude model for the dielectric function of Fe(Te,Se), a multiband superconductor, and fitting the absolute optical reflection spectra using the transfer matrix method. A high extinction coefficient in the visible to near-infrared range makes nanometer-thin Fe(Te,Se) flakes a promising material for photodetection applications., Comment: 18 Pages, 4 Figures

How do update rules affect the dynamical and steady state properties of a flock? In this study, we have explored the active Ising spins (s = +-1) in one dimension, where spin updates its orientation according to the Metropolis algorithm (based on the neighbors) via two different update rules. (i) Parallel, and (ii) Random-sequential. We explore the effect of Parallel and Random-sequential updates on the dynamical properties of flocks in one dimension. Due to the inherent asynchronous nature of the Random-sequential update, the directional switching of the flock is increased compared to the Parallel one. The nature of phase transition is affected by the difference in the updating mechanism: discontinuous for Parallel and continuous for Random-sequential updates., Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1704.04041

We study the {\sc Uniform Circle Formation} ({\sc UCF}) problem for a swarm of $n$ autonomous mobile robots operating in \emph{Look-Compute-Move} (LCM) cycles on the Euclidean plane. We assume our robots are \emph{luminous}, i.e. embedded with a persistent light that can assume a color chosen from a fixed palette, and \emph{opaque}, i.e. not able to see beyond a collinear robot. Robots are said to \emph{collide} if they share positions or their paths intersect within concurrent LCM cycles. To solve {\sc UCF}, a swarm of $n$ robots must autonomously arrange themselves so that each robot occupies a vertex of the same regular $n$-gon not fixed in advance. In terms of efficiency, the goal is to design an algorithm that optimizes (or provides a tradeoff between) two fundamental performance metrics: \emph{(i)} the execution time and \emph{(ii)} the size of the color palette. There exists an $O(1)$-time $O(1)$-color algorithm for this problem under the fully synchronous and semi-synchronous schedulers and a $O(\log\log n)$-time $O(1)$-color or $O(1)$-time $O(\sqrt{n})$-color algorithm under the asynchronous scheduler, avoiding collisions. In this paper, we develop a deterministic algorithm solving {\sc UCF} avoiding collisions in $O(1)$-time with $O(1)$ colors under the asynchronous scheduler, which is asymptotically optimal with respect to both time and number of colors used, the first such result. Furthermore, the algorithm proposed here minimizes for the first time what we call the \emph{computational SEC}, i.e. the smallest circular area where robots operate throughout the whole algorithm., Comment: 33 pages, 15 figures

In this work, we investigate the effects of chirality, accounting for translational diffusion, on active Brownian particles in two and three dimensions. Despite the inherent complexity in solving the Fokker-Planck equation, we demonstrate a Laplace transform method for precisely calculating the temporal evolution of various dynamic moments. Our analysis yields explicit expressions for multiple moments, such as the second and fourth moments of displacement, revealing the impact of persistence and chirality. These moments exhibit oscillatory behaviour, and excess kurtosis indicates deviations from the Gaussian distribution during intermediate time intervals., Comment: 27 pages, 8 figures

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for $\mathfrak{sl}(m+1,n+1)$, $\mathfrak{osp}(2,2n)$, $G(3)$ and $F(4)$ under an additional assumption. This result is a Lie superalgebra analogue of Rajan's fundamental result \cite{MR2123935} on unique factorization of tensor products for finite dimensional complex simple Lie algebras., Comment: Preliminary version, suggestions and comments are welcome, 20pages

We perform a comprehensive study on the role of thermal noise on the ordering kinetics of a collection of active Brownian particles modeled using coarse-grained conserved active model B (AMB). The ordering kinetics of the system is studied for the critical mixture when quenched from high to a low temperature. The structure of the growing domains changes from isolated droplet type for AMB without noise to bi-continuous type for active model B with noise (AMBN). Unlike the passive counterpart of the AMB, the noise is relevant for the growth kinetics of the AMB. We use extensive numerical study, as well as dynamic scaling hypothesis to characterize the kinetics of the system. We find that the asymptotic growth law for AMBN is diffusive Lifshitz-Slyozov (LS) type, whereas it was reported previously that the asymptotic growth law for the AMB without noise is slower, with a growth exponent 4. Moreover, the kinetics of the growing domains show a strong time dependent growth for AMBN. The growth law shows a crossover from early time 1/3 value to intermediate time 1/4 value, and it again traverses from 1/4 to 1/3 asymptotically. The two different scaling functions are found for intermediate time and late time with growth law 1/4 and 1/3 respectively., Comment: 9 Pages, 7 figures

We consistently observe a unique pattern in remanence in a number of canted-antiferromagnets (AFM) and piezomagnets. A part of the remanence is $\textit{quasi-static}$ in nature and vanishes above a critical magnetic field. Present work is devoted to exploring this $\textit{quasi-static}$ remanence ($\mu$) in a series of isostructural canted-AFMs and piezomagnets that possess progressively increasing N\'eel temperature ($T{_N}$). Comprehensive investigation of remanence as a function of $\textit{magnetic-field}$ and $\textit{time}$ in CoCO$_{3}$, NiCO$_{3}$ and MnCO$_{3}$ reveals that the magnitude of $\mu$ increases with decreasing $T{_N}$, but the stability with time is higher in the samples with higher $T{_N}$. Further to this, all three carbonates exhibit a universal scaling in $\mu$, which relates to the concurrent phenomenon of piezomagnetism. Overall, these data not only establish that the observation of $\textit{quasi-static}$ remanence with $\textit{counter-intuitive}$ magnetic-field dependence can serve as a foot-print for spin-canted systems, but also confirms that simple remanence measurements, using SQUID magnetometry, can provide insights about the extent of spin canting - a non trivial parameter to determine. In addition, these data suggest that the functional form of $\mu$ with $\textit{magnetic-field}$ and $\textit{time}$ may hold key to isolate Dzyaloshinskii Moriya Interaction driven spin-canted systems from Single Ion Anisotropy driven ones. We also demonstrate the existence of $\mu$ by tracking specific peaks in neutron diffraction data, acquired in remnant state in CoCO$_{3}$.

We consider the task of computing functions $f: \mathbb{N}^k\to \mathbb{N}$, where $ \mathbb{N}$ is the set of natural numbers, by finite teams of agents modelled as deterministic finite automata. The computation is carried out in a distributed way, using the {\em discrete half-line}, which is the infinite graph with one node of degree 1 (called the root) and infinitely many nodes of degree 2. The node at distance $j$ from the root represents the integer $j$. We say that a team $\mathcal{A}^f$ of automata computes a function $f$, if in the beginning of the computation all automata from $\mathcal{A}^f$ are located at the arguments $x_1,\dots,x_k$ of the function $f$, in groups $\mathcal{A}^f _j$ at $x_j$, and at the end, all automata of the team gather at $f(x_1,\dots,x_k)$ and transit to a special state $STOP$. At each step of the computation, an automaton $a$ can ``see'' states of all automata colocated at the same node: the set of these states forms an input of $a$. Our main result shows that, for every primitive recursive function, there exists a finite team of automata that computes this function. We prove this by showing that basic primitive recursive functions can be computed by teams of automata, and that functions resulting from the operations of composition and of primitive recursion can be computed by teams of automata, provided that the ingredient functions of these operations can be computed by teams of automata. We also observe that cooperation between automata is necessary: even some very simple functions $f: \mathbb{N}\to \mathbb{N}$ cannot be computed by a single automaton.

Treasure hunt and rendezvous are fundamental tasks performed by mobile agents in graphs. In treasure hunt, an agent has to find an inert target (called treasure) situated at an unknown node of the graph. In rendezvous, two agents, initially located at distinct nodes of the graph, traverse its edges in synchronous rounds and have to meet at some node. We assume that the graph is connected (otherwise none of these tasks is feasible) and consider deterministic treasure hunt and rendezvous algorithms. The time of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until the treasure is found. The time of a rendezvous algorithm is the worst-case number of rounds since the wakeup of the earlier agent until the meeting. To the best of our knowledge, all known treasure hunt and rendezvous algorithms rely on the assumption that degrees of all nodes are finite, even when the graph itself may be infinite. In the present paper we remove this assumption for the first time, and consider both above tasks in arbitrary connected graphs whose nodes can have either finite or countably infinite degrees. Our main result is the first universal treasure hunt algorithm working for arbitrary connected graphs. We prove that the time of this algorithm has optimal order of magnitude among all possible treasure hunt algorithms working for arbitrary connected graphs. As a consequence of this result we obtain the first universal rendezvous algorithm working for arbitrary connected graphs. The time of this algorithm is polynomial in a lower bound holding in many graphs, in particular in the tree all of whose degrees are infinite.

Temperature plays a very important role in various biological processes like the evolution of life, as it is anticipated that early life existed in a very hot environment that eventually cooled down with time. In vitro experiments, conducted with various active matter systems in anisotropic temperature environments, show several interesting outcomes. Motivated by these experiments and some simulation results, we study the collective behavior of self-propelled hard rods with excluded volume interactions, moving on a substrate in two dimensions and subjected to a small but finite external temperature gradient. Using a coarse-grained hydrodynamic approach, we explore the behavior of the system in the steady state and the stability both in the passive and active limits.