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A long-standing challenge is the design of chips resilient to faults and glitches. Both fine-grained gate diversity and coarse-grained modular redundancy have been used in the past. However, these approaches have not been well-studied under other threat models where some stakeholders in the supply chain are untrusted. Increasing digital sovereignty tensions raise concerns regarding the use of foreign off-the-shelf tools and IPs, or off-sourcing fabrication, driving research into the design of resilient chips under this threat model. This paper addresses a threat model considering three pertinent attacks to resilience: distribution, zonal, and compound attacks. To mitigate these attacks, we introduce the \texttt{ResiLogic} framework that exploits \textit{Diversity by Composability}: constructing diverse circuits composed of smaller diverse ones by design. This gives designer the capability to create circuits at design time without requiring extra redundancy in space or cost. Using this approach at different levels of granularity is shown to improve the resilience of circuit design in \texttt{ResiLogic} against the three considered attacks by a factor of five. Additionally, we also make a case to show how E-Graphs can be utilized to generate diverse circuits under given rewrite rules.

Computational offload to hardware accelerators is gaining traction due to increasing computational demands and efficiency challenges. Programmable hardware, like FPGAs, offers a promising platform in rapidly evolving application areas, with the benefits of hardware acceleration and software programmability. Unfortunately, such systems composed of multiple hardware components must consider integrity in the case of malicious components. In this work, we propose Samsara, the first secure and resilient platform that derives, from Byzantine Fault Tolerant (BFT), protocols to enhance the computing resilience of programmable hardware. Samsara uses a novel lightweight hardware-based BFT protocol for Systems-on-Chip, called H-Quorum, that implements the theoretical-minimum latency between applications and replicated compute nodes. To withstand malicious behaviors, Samsara supports hardware rejuvenation, which is used to replace, relocate, or diversify faulty compute nodes. Samsara's architecture ensures the security of the entire workflow while keeping the latency overhead, of both computation and rejuvenation, close to the non-replicated counterpart., Comment: To be published in The 43rd International Symposium on Reliable Distributed Systems (SRDS 2024)

To cope with the ever increasing threats of dynamic and adaptive persistent attacks, Fault and Intrusion Tolerance (FIT) is being studied at the hardware level to increase critical systems resilience. Based on state-machine replication, FIT is known to be effective if replicas are compromised and fail independently. This requires different ways of diversification at the software and hardware levels. In this paper, we introduce the first hardware-based rejuvenation framework, we call Samsara, that allows for creating new computing cores (on which FIT replicas run) with diverse architectures. This is made possible by taking advantage of the programmable and reconfigurable features of MPSoC with an FPGA. A persistent attack that analyzes and exploits the vulnerability of a core will not be able to exploit it as rejuvenation to a different core architecture is made fast enough. We discuss the feasibility of this design, and we leave the empirical evaluations for future work.

Managing inputs that are novel, unknown, or out-of-distribution is critical as an agent moves from the lab to the open world. Novelty-related problems include being tolerant to novel perturbations of the normal input, detecting when the input includes novel items, and adapting to novel inputs. While significant research has been undertaken in these areas, a noticeable gap exists in the lack of a formalized definition of novelty that transcends problem domains. As a team of researchers spanning multiple research groups and different domains, we have seen, first hand, the difficulties that arise from ill-specified novelty problems, as well as inconsistent definitions and terminology. Therefore, we present the first unified framework for formal theories of novelty and use the framework to formally define a family of novelty types. Our framework can be applied across a wide range of domains, from symbolic AI to reinforcement learning, and beyond to open world image recognition. Thus, it can be used to help kick-start new research efforts and accelerate ongoing work on these important novelty-related problems. This extended version of our AAAI 2021 paper included more details and examples in multiple domains., Comment: Extended version/preprint of a AAAI 2021 paper

Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Inspired by the exact 0-1 integer linear programming formalism from the recent literature, we propose a new methods to obtain upper bounds for the geodetic number in an algorithmic way. The efficiency of these algorithms are demonstrated on a collection of structurally different graphs.

In this paper, we have studied the gravitational baryogenesis of isotropic and homogeneous universe in the frame-work of general relativity. We investigate an exact and new solution of Einstein's field equations for FRW metric. Our solution represents a transitioning model of the universe which was expanding in decelerated mode and it transit in accelerated mode after dominance of cosmological constant $\Lambda$. We observe that gravitational baryogenesis occurs in the derived universe and derived baryon entropy ratio is in good agreement with its observational value., Comment: 8 Pages, 4 Figures, Accepted in Gravitation and Cosmology

We show the physical realization and experimental demonstration of an exceptional point of 6th order degeneracy in a triple ladder (or three-way) microwave waveguide realized using three coupled microstrips on a grounded dielectric substrate. This threeway waveguide supports six Bloch eigenmodes and all coalesce onto a degenerate single eigenmode at a given frequency. The three-way waveguide is gainless, and this exceptional point is associated to a vanishing group velocity and its multiple derivatives. Indeed the wavenumber-frequency dispersion diagram, that we call 6th order degenerate band edge (6DBE) has six coalescing branches. We provide the experimental verification of a 6th order exceptional point by evaluating the degenerate wavenumber-frequency dispersion diagram from the measurement of scattering parameters of a six-port unit cell. We also show the resonant behavior of a cavity made of the three-way waveguide with finite length. The unique properties of 6DBE can be exploited in designing innovative high-Q resonators, oscillators, filters, and pulse shaping devices.

This paper intends to obtain concircular vector fields of Kantowski Sachs and Bianch type III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski Sachs and Bianchi type III spacetimes admit four, six, or fifteen dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation., Comment: 21 pages, 23 References

In this paper, we search the existence of invariant solutions of Bianchi type I space-time in the context of $f\left(R,T\right)$ gravity. The exact solution of the Einstein's field equations are derived by using Lie point symmetry analysis method that yield two models of invariant universe for symmetries $X^{(1)}$ and $X^{(3)}$. The model with symmetries $X^{(1)}$ begins with big bang singularity while the model with symmetries $X^{(3)}$ does not favour the big bang singularity. Under this specification, we find out at set of singular and non singular solution of Bianchi type I model which present several other physically valid features within the framework of $f\left(R,T\right)$., Comment: 14 Pages, 2 Figure panels, Textual changes and 01 reference added

In this paper, a novel process has been developed to realize high-level complex cognitive behaviors into reactive agents, efficiently. This method paves the way for deducting high-level reactive behaviors from low-level perceptive information by autonomous robots. The aforementioned process lets us actualize different generations of Braitenberg vehicles, are which able to mimic desired behaviors to survive in complex environments with high degrees of flexibility in perception and emergence of high-level cognitive actions. The approach has been used to engineer a Braitenberg vehicle with a wide range of perception-action capabilities. Verification would be realized within this framework, due to the efficient traceability between each sequential pair of process phases. The applied simulations demonstrate the efficiency of the established development process, based on the Braitenberg vehicle's behavior., Comment: 5 pages, 7 figures

In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the similarity reductions and obtain exact solutions in connection to the evolutionary scenario of the universe. The special feature of the study is that it deals with the electromagnetic energy of the inhomogeneous universe through the non-vanishing component of electromagnetic field tensor $F_{12}$ and assumes that the free gravitational field is of Petrov type-II non-degenerate. We have found that the electromagnetic field tensor is positive and increasing function of time. To validate the solution set, we examine with detailed discussions several physical as well as geometrical features of a specific sub-case of the model., Comment: 16 pages, 3 figures, Published version

This article explores the Conformal Ricci Collineations (CRCs) for the plane-symmetric static spacetime. The non-linear coupled CRC equations are solved to get the general form of conformal Ricci symmetries. In the non-degenerate case, it turns out that the dimension of the Lie algebra of CRCs is finite. In the case were the Ricci tensor is degenerate, it found that the algebra of CRCs for the plane-symmetric static spacetime is mostly, but not always, infinite dimensional. In one case of degenerate Ricci tensor, we solved the differential constraints completely and a spacetime metric is obtained along with CRCs. We found ten possible cases of finite and infinite dimensional Lie algebras of CRCs for the considered spacetime., Comment: 17 pages

We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the deviation of pressure from isotropy. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system of one-dimensional subalgebras. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analyzed. We solve the Einstein field equations, described by a system of non-linear partial differential equations (NLPDEs), by using the Lie point symmetry analysis method. The geometrical and kinematical features of the models and the behavior of the anisotropy of dark energy, are examined in detail., Comment: 10 pages, 2 figure panels, Textual changes and References updated

In this paper Bianchi type I spacetimes are completely classified by their homothetic vectors in the context of Lyra geometry. The non-linear coupled Lyra homothetic equations are obtained and solved completely for different cases. In some cases, Bianchi type I spacetimes admit proper Lyra homothetic vectors (LHVs) for special choices of the metric functions, while there exist other cases where the spacetime under consideration admits only Lyra Killing vectors (LKVs). In all the possible cases where Bianchi type I spacetimes admit proper LHVs or LKVs, we obtained homothetic and Killing vectors for Bianchi type I spacetimes in general relativity by taking the displacement vector of Lyra geometry as zero. Matter collineation symmetry is explained by taking the matter field as a perfect fluid. The obtained proper LHVs and LKVs are used in matter collineation equations and a barotropic equation of state having $\rho(t)\,=\,\gamma\,p(t)$, $0\,\leq\,\gamma\,\leq\,1$ form is always obtained when the displacement vector is considered as a function of $t$ or treated as a constant., Comment: 21 pages, Section 3 is added, Some new notations are introduced and results are improved

In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and eometrical properties of the models derived in the paper. The solutions, at least one of them, are interesting physically as they can explain the accelerating as well as singularity free Universe., Comment: Published in Phys.Scripta 89 (2014) 11, 115206. arXiv admin note: text overlap with arXiv:1405.3185, arXiv:1305.4631

In this paper, we derive some new invariant solutions of dark energy models in cylindrically symmetric space-time. To quantify the deviation of pressure from isotropy, we introduce three different time dependent skewness parameters along the spatial directions. The matter source consists of dark energy which is minimally interact with perfect fluid. We use symmetry analysis method for solving the non-linear partial differential equations (NLPDEs) which is more powerful than the classical methods of solving NLPDEs. The geometrical and kinematical features of the models and the behaviour of the anisotropy of dark energy, are examined in detail., Comment: 13 pages

The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been obtained by considering the inhomogeneous nature of metric potential. The physical behavior and geometrical aspects of the derived models are also discussed., Comment: 12 pages, 1 figures

Inhomogeneous Bianchi type-I cosmological model with electro-magnetic field based on Lyra geometry is investigated. Using separated method, the Einstein field equations have been solved analytically with the aid of Mathematica programm. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. We have assumed that F(12) is the only non-vanishing component of electro-magnetic field tensor F(ij). The Maxwells equations show that F(12) is the function of x alone whereas the magnetic permeability is the function of x and t both. To get the deterministic solution, it has been assumed that the expansion scaler Theta in the model is proportional to the value sigma(11) of the shear tensor sigma(ij). Some physical and geometric properties of the model are also discussed and graphed., Comment: Int. J. Theor. Phys. 52, 4055 (2013)

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. The isovector fields of Einstein's field equation for the models under consideration are derived. A new class of exact solutions of Einstein's field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail., Comment: 13 pages

We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions., Comment: 12 pages and 2 figure

In this paper, we define a new special curve in Euclidean 3-space which we call {\it $k-$slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we have given some necessary and sufficient conditions for the $k-$slant helix., Comment: 13 pages only

In this paper, we define a new family of curves and call it a {\it family of similar curves with variable transformation} or briefly {\it SA-curves}. Also we introduce some characterizations of this family and we give some theorems. This definition introduces a new classification of a space curve. Also, we use this definition to deduce the position vectors of plane curves, general helices and slant helices, as examples of a similar curves with variable transformation., Comment: 13 pages only

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrinsic equations. Moreover, we give some examples to illustrate how to find the position vectors of a spacelike general helices with a spacelike and timelike principal normal vector from the intrinsic equations., Comment: 15 pages, 3 figures

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented., Comment: 11 pages only

In this paper we consider the equiform motion of a helix in Euclidean space $\mathbf{E}^7$. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$ is constant. Under this assumption, we prove that if the scalar curvature $\mathbf{K}$ is constant, then $\mathbf{K}$ must equal zero., Comment: 11 pages, 1 figure

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations $\kappa=\kappa(s)$ and $\tau=\tau(s)$ (where $\kappa$ and $\tau$ are the curvature and torsion of the space curve $\psi$, respectively) is still open \cite{eisenh, lips}. However, in the case of a plane curve, helix and general helix, this problem is solved. In this paper, we solved this problem in the case of a slant helix. Also, we applied this method to find the representation of a Salkowski, anti-Salkowski curves and a curve of constant precession, as examples of a slant helices, by means of intrinsic equations., Comment: 14 pages, 3 figures

In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E$^3_1$ satisfies a vector differential equation of fourth order. The general solution of mentioned vector differential equation has not yet been found. By special cases, we determine the parametric representation of the general helices from the intrinsic equations (i.e. curvature and torsion are functions of arc-length) of the time-like curve. Moreover, we give some examples to illustrate how to find the position vector from the intrinsic equations of general helices., Comment: p pages 3 figures

Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\e^3$. In this paper, we adapt definition of such curves to time-like curves in Minkowski 3-space $\e_1^3$. Thereafter, we introduce an explicit parametrization of a time-like Salkowski curves and a time-like Anti-Salkowski curves in Minkowski space $\e_1^3$. Also, we characterize them as space curve with constant curvature or constant torsion and whose normal vector makes a constant angle with a fixed line., Comment: 9 pages only

In this paper we consider the equiform motion of a sphere in Euclidean space $\mathbf{E}^7$. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$ is constant. Under this assumption, we prove that $|\mathbf{K}|<2$., Comment: 11 pages olly

In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of their curvature functions., Comment: 11 pages only

In this paper, we prove that the position vector of every space curve satisfies a vector differential equation of fourth order. Also, we determine the parametric representation of the position vector $\psi=\Big(\psi_1,\psi_2,\psi_3\Big)$ of general helices from the intrinsic equations $\kappa=\kappa(s)$ and $\tau=\tau(s)$ where $\kappa$ and $\tau$ are the curvature and torsion of the space curve $\psi$, respectively. Our result extends some knwown results. Moreover, we give four examples to illustrate how to find the position vector from the intrinsic equations of general helices., Comment: 10 pages only

We consider a unit speed curve $\alpha$ in Euclidean four-dimensional space $E^4$ and denote the Frenet frame by $\{T,N,B_1,B_2\}$. We say that $\alpha$ is a slant helix if its principal normal vector $N$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures., Comment: 9 pages

We consider a unit speed curve $\alpha$ in Euclidean $n$-dimensional space $E^n$ and denote the Frenet frame by $\{v_1,...,v_n\}$. We say that $\alpha$ is a cylindrical helix if its tangent vector $v_1$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures., Comment: 10 pages

We consider a curve $\alpha=\alpha(s)$ in Minkowski 3-space $E_1^3$ and denote by $\{T,N,B}$ the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction $U$ of $E_1^3$ such that the function $$ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$., Comment: 7 pages

We consider a unit speed timelike curve $\alpha$ in Minkowski 4-space $E_1^4$ and denote the Frenet frame of $\alpha$ by $\{T,N,B_1,B_2\}$. We say that $\alpha$ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of $E_1^4$. In this work we study those helices where the function $$ is constant and we give different characterizations of such curves., Comment: 10 pages