arXiv subjects

Manish Kumar

Publications and source records attributed to Manish Kumar.

At least 91 records · Page 5Linked to original sources

arXiv2024

Agent-based Leader Election, MST, and Beyond

Leader election is one of the fundamental and well-studied problems in distributed computing. In this paper, we initiate the study of leader election using mobile agents. Suppose $n$ agents are positioned initially arbitrarily on the nodes of an arbitrary, anonymous, $n$-node, $m$-edge graph $G$. The agents relocate themselves autonomously on the nodes of $G$ and elect an agent as a leader such that the leader agent knows it is a leader and the other agents know they are not leaders. The objective is to minimize time and memory requirements. Following the literature, we consider the synchronous setting in which each agent performs its operations synchronously with others and hence the time complexity can be measured in rounds. The quest in this paper is to provide solutions without agents knowing any graph parameter, such as $n$, a priori. We first establish that, without agents knowing any graph parameter a priori, there exists a deterministic algorithm to elect an agent as a leader in $O(m)$ rounds with $O(n\log n)$ bits at each agent. Using this leader election result, we develop a deterministic algorithm for agents to construct a minimum spanning tree of $G$ in $O(m+n\log n)$ rounds using $O(n \log n)$ bits memory at each agent, without agents knowing any graph parameter a priori. Finally, using the same leader election result, we provide improved time/memory results for other fundamental distributed graph problems, namely, gathering, maximal independent set, and minimal dominating sets, removing the assumptions on agents knowing graph parameters a priori.

cs.DC↗

arXiv2024

Optimizing Robot Dispersion on Grids: with and without Fault Tolerance

The introduction and study of dispersing mobile robots across the nodes of an anonymous graph have recently gained traction and have been explored within various graph classes and settings. While optimal dispersion solution was established for {\em oriented} grids [Kshemkalyani et al., WALCOM 2020], a significant unresolved question pertains to whether achieving optimal dispersion is feasible on an {\em unoriented} grid. This paper investigates the dispersion problem on unoriented grids, considering both non-faulty and faulty robots. The challenge posed by unoriented grids lies in the absence of a clear sense of direction for a single robot moving between nodes, as opposed to the straightforward navigation of oriented grids. We present three deterministic algorithms tailored to our robot model. The first and second algorithms deal with the dispersion of faulty and non-faulty robots, ensuring both time and memory optimization in oriented and unoriented grids, respectively. Faulty robots that are prone to crashing at any time, causing permanent failure. In both settings, we achieve dispersion in $O(\sqrt{n})$ rounds while requiring $O(\log n)$ bits of memory per robot. The third algorithm tackles faulty robots prone to crash faults in an unoriented grid. In this scenario, our algorithm operates within $O(\sqrt{n} \log n)$ time and uses $O(\sqrt{n} \log n)$ bits of memory per robot. The robots need to know the value of $n$ for termination.

cs.DC↗

arXiv2024

Bertini type results and their applications

We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse \ell-adic sheaves on the variety with "ramification bounded by a branch data" remains irreducible when restricted to the curve.

math.AG↗

arXiv2024

Pocket Schlieren: a background oriented schlieren imaging platform on a smartphone

Background-oriented schlieren (BOS) is a powerful technique for flow visualization. Nevertheless, the widespread dissemination of BOS is impeded by its dependence on scientific cameras, computing hardware, and dedicated analysis software. In this work, we aim to democratize BOS by providing a smartphone based scientific tool called "Pocket Schlieren". Pocket Schlieren enables users to directly capture, process, and visualize flow phenomena on their smartphones. The underlying algorithm incorporates consecutive frame subtraction (CFS) and optical flow (OF) techniques to compute the density gradients inside a flow. It performs on both engineered and natural background patterns. Using Pocket Schlieren, we successfully visualized the flow produced from a burning candle flame, butane lighter, hot soldering iron, room heater, water immersion heating rod, and a large outdoor butane flame. Pocket Schlieren promises to serve as a frugal yet potent instrument for scientific and educational purposes. We have made it publicly available at doi: 10.5281/zenodo.10949271.

cs.HC↗

arXiv2024

Characterization of genuine ramification using formal orbifolds

We give a characterization of genuinely ramified maps of formal orbifolds in the Tannakian framework. In particular we show that a morphism is genuinely ramified if and only if the pullback of every stable bundle remains stable in the orbifold category. We also give some other characterizations of genuine ramification. This generalizes the results of [BKP1] and [BP1]. In fact, it is a positive characteristic analogue of results in [BKP2].

math.AG↗

arXiv2024

Multi Agent Pathfinding for Noise Restricted Hybrid Fuel Unmanned Aerial Vehicles

Multi Agent Path Finding (MAPF) seeks the optimal set of paths for multiple agents from respective start to goal locations such that no paths conflict. We address the MAPF problem for a fleet of hybrid-fuel unmanned aerial vehicles which are subject to location-dependent noise restrictions. We solve this problem by searching a constraint tree for which the subproblem at each node is a set of shortest path problems subject to the noise and fuel constraints and conflict zone avoidance. A labeling algorithm is presented to solve this subproblem, including the conflict zones which are treated as dynamic obstacles. We present the experimental results of the algorithms for various graph sizes and number of agents.

math.OC↗

arXiv2024

Pushforward of structure sheaf and virtual global generation

Let $f:X\rightarrow Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is virtually globally generated. Moreover, $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is ample if and only if $f$ is genuinely ramified.

math.AG↗

arXiv2024

A criterion for solving embedding problems for the etale fundamental group of curves

Let $C$ be an affine curve over an algebraically closed field $k$ of characteristic $p>0$. Given an embedding problem $(β:Γ\longrightarrow G, α: π^{et}_1(C)\longrightarrow G)$ for $π_1^{et}(C)$ where $β$ is a surjective homomorphism of finite groups with prime-to-$p$ kernel $H$, we discuss when an $H$-cover of the $G$-cover of $C$ corresponding to $α$ is a solution. When $H$ is abelian and $G$ is a $p$-group, some necessary and sufficient conditions for the solvability of the embedding problem are given in terms of the action of $G$ on certain generalized Picard group.

math.AG↗

arXiv2024

Noise Aware Path Planning and Power Management of Hybrid Fuel UAVs

Hybrid fuel Unmanned Aerial Vehicles (UAV), through their combination of multiple energy sources, offer several advantages over the standard single fuel source configuration, the primary one being increased range and efficiency. Multiple power or fuel sources also allow the distinct pitfalls of each source to be mitigated while exploiting the advantages within the mission or path planning. We consider here a UAV equipped with a combustion engine-generator and battery pack as energy sources. We consider the path planning and power-management of this platform in a noise-aware manner. To solve the path planning problem, we first present the Mixed Integer Linear Program (MILP) formulation of the problem. We then present and analyze a label-correcting algorithm, for which a pseudo-polynomial running time is proven. Results of extensive numerical testing are presented which analyze the performance and scalability of the labeling algorithm for various graph structures, problem parameters, and search heuristics. It is shown that the algorithm can solve instances on graphs as large as twenty thousand nodes in only a few seconds.

math.OC↗

arXiv2024

Genuinely ramified maps and monodromy

For any genuinely ramified morphism $f\, :\, Y\, \longrightarrow\, X$ between irreducible smooth projective curves we prove that $\overline{(Y\times_X Y) \setminus Δ}$ is connected, where $Δ\, \subset\, Y\times_X Y$ is the diagonal. Using this result the following are proved: If $f$ is further Morse then the Galois closure is the symmetric group $S_d$, where $d\,=\, \text{degree}(f)$. The Galois group of the general projection, to a line, of any smooth curve $X\,\subset\, \PP^n$ of degree $d$, which is not contained in a hyperplane and contains a non-flex point, is $S_d$.

math.AG↗

arXiv2024

Ramified covering maps of singular curves and stability of pulled back bundles

Let $f : X \rightarrow Y$ be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is étale on an open subset of $Y$ that contains both the singular locus of $Y$ and the image, in $Y$, of the singular locus of $X$. We prove that the following statements are equivalent: \begin{enumerate} \item The homomorphism of étale fundamental groups $$f_* : π_1^{\rm et}(X) \rightarrowπ_1^{\rm et}(Y)$$ induced by $f$ is surjective. \item There is no nontrivial étale covering $ϕ: Y' \rightarrow Y$ admitting a morphism $q: X \rightarrow Y'$ such that $ϕ\circ q = f$. \item The fiber product $X\times_Y X$ is connected. \item $\dim H^0(X, f^*f_* {\mathcal O}_X)= 1$. \item ${\mathcal O}_Y \subset f_*{\mathcal O}_X$ is the maximal semistable subsheaf. \item The pullback $f^*E$ of every stable sheaf $E$ on $Y$ is also stable. \end{enumerate}

math.AG↗

arXiv2023

Investigating the orbital evolution of the eccentric HMXB GX 301$-$2 using long-term X-ray lightcurves

We report the orbital decay rate of the high mass X-ray binary GX 301$-$2 from an analysis of its long-term X-ray light curves and pulsed flux histories from CGRO/BATSE, RXTE/ASM, Swift/BAT, Fermi/GBM and MAXI by timing the pre-periastron flares over a span of almost 30 years. The time of arrival of the pre-periastron flares exhibits an energy dependence (hard lag) and the orbital period decay was estimated after correcting for it. This method of orbital decay estimation is unaffected by the fluctuations in the spin rate of the X-ray pulsar associated with variations in the mass accretion rate. The resulting $\dot P_\textrm{orb}$ $=-(1.98\pm0.28)\times10^{-6}$ s s$^{-1}$ indicates a rapid evolution timescale of $|P_\textrm{orb}/\dot P_\textrm{orb}|\sim 0.6\times10^{5}$ yr, making it the high mass X-ray binary with the fastest orbital decay. Our estimate of $\dot P_\mathrm{orb}$ is off by a factor of $\sim2$ from the previously reported value of $-(3.7\pm0.5)\times10^{-6}$ s s$^{-1}$ estimated from pulsar TOA analysis. We discuss various possible mechanisms that could drive this rapid orbital decay and also suggest that GX 301$-$2 is a prospective Thorne-Żytkow candidate.

astro-ph.HE↗

arXiv2023

Identifying the origin of delayed electroluminescence in a polariton organic light-emitting diode

Modifying the energy landscape of existing molecular emitters is an attractive challenge with favourable outcomes in chemistry and organic optoelectronic research. It has recently been explored through strong light-matter coupling studies where the organic emitters were placed in an optical cavity. Nonetheless, a debate revolves around whether the observed change in the material properties represents novel coupled system dynamics or the unmasking of pre-existing material properties induced by light-matter interactions. Here, for the first time, we examined the effect of strong coupling in polariton organic light-emitting diodes via time-resolved electroluminescence studies. We accompanied our experimental analysis with theoretical fits using a model of coupled rate equations accounting for all major mechanisms that can result in delayed electroluminescence in organic emitters. We found that in our devices the delayed electroluminescence was dominated by emission from trapped charges and this mechanism remained unmodified in the presence of strong coupling.

cond-mat.mtrl-sci↗

arXiv2023

Multi-orbital Kondo screening in strongly correlated polyradical nanographenes

We discuss coexistence of Kondo and spin excitation signals in tunneling spectroscopy in strongly correlated polyradical $π$-magnetic nanographenes on a metal surface. The Kondo signal is rationalized by a multi-orbital Kondo screening of the unpaired electrons. The fundamental processes are spin-flips of antiferromagnetic (AFM) order involving charged molecular multiplets. We introduce a~perturbative model, which provides simple rules to identify the presence of AFM channels responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. This framework can be applied to similar strongly correlated open-shell systems.

cond-mat.str-el↗

arXiv2023

Conjugate variables approach to mixed $q$-Araki-Woods algebras: Factoriality and non-injectivity

We establish factoriality and non-injectivity in full generality for the mixed $q$-Araki-Woods von Neumann algebra associated to a separable real Hilbert space $\mathsf{H}_{\mathbf{R}}$ with $\dim\mathsf{H}_{\mathbf{R}}\geq 2$, a strongly continuous one parameter group of orthogonal transformations on $\mathsf{H}_\mathbb{R}$, a direct sum decomposition $\mathsf{H}_{\mathbf{R}}=\oplus_{i}\mathsf{H}_{\mathbb{R}}^{(i)}$, and a real symmetric matrix $(q_{ij})$ with $q=\sup_{i,j}|q_{ij}|<1$. This is achieved by first proving the existence of conjugate variables for a finite number of generators of the algebras, following the lines of Miyagawa-Speicher and Kumar-Skalski-Wasilewski. The conjugate variables belong to the factors in question and satisfy certain Lipschitz condition.

math.OA↗

arXiv2023

Security of XCB and HCTR

Tweakable Enciphering Scheme (TES) is a length preserving scheme which provides confidentiality and admissible integrity. XCB (Extended Code Book) is a TES which was introduced in 2004. In 2007, it was modified and security bound was provided. Later, these two versions were referred to as XCBv1 and XCBv2 respectively. XCBv2 was proposed as the IEEE-std 1619.2 2010 for encryption of sector oriented storage media. In 2013, first time Security bound of XCBv1 was given and XCBv2's security bound was enhanced. A constant of $2^{22}$ appears in the security bounds of the XCBv1 and XCBv2. We showed that this constant of $2^{22}$ can be reduced to $2^{5}$. Further, we modified the XCB (MXCB) scheme such that it gives better security bound compared to the present XCB scheme. We also analyzed some weak keys attack on XCB and a type of TES known as HCTR (proposed in 2005). We performed distinguishing attack and the hash key recovery attack on HCTR. Next, we analyzed the dependency of the two different keys in HCTR.

cs.CR↗

arXiv2023

Sublinear Message Bounds of Authenticated Implicit Byzantine Agreement

This paper studies the message complexity of authenticated Byzantine agreement (BA) in synchronous, fully-connected distributed networks under an honest majority. We focus on the so-called {\em implicit} Byzantine agreement problem where each node starts with an input value and at the end a non-empty subset of the honest nodes should agree on a common input value by satisfying the BA properties (i.e., there can be undecided nodes). We show that a sublinear (in $n$, number of nodes) message complexity BA protocol under honest majority is possible in the standard PKI model when the nodes have access to an unbiased global coin and hash function. In particular, we present a randomized Byzantine agreement algorithm which, with high probability achieves implicit agreement, uses $\tilde{O}(\sqrt{n})$ messages, and runs in $\tilde{O}(1)$ rounds while tolerating $(1/2 - ε)n$ Byzantine nodes for any fixed $ε> 0$, the notation $\Tilde{O}$ hides a $O(\polylog{n})$ factor. The algorithm requires standard cryptographic setup PKI and hash function with a static Byzantine adversary. The algorithm works in the CONGEST model and each node does not need to know the identity of its neighbors, i.e., works in the $KT_0$ model. The message complexity (and also the time complexity) of our algorithm is optimal up to a $\polylog n$ factor, as we show a $Ω(\sqrt{n})$ lower bound on the message complexity.

cs.DC↗

arXiv2023

Quot schemes and Fourier-Mukai transformation

We consider several related examples of Fourier-Mukai transformations involving the quot scheme. A method of showing conservativity of these Fourier-Mukai transformations is described.

math.AG↗