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  • The Internet of Things (IoT) being a promising technology of the future is expected to connect billions of devices. The increased number of communication is expected to generate mountains of data and the security of data can be a threat. The devices in the architecture are essentially smaller in size and low powered. Conventional encryption algorithms are generally computationally expensive due to their complexity and requires many rounds to encrypt, essentially wasting the constrained energy of the gadgets. Less complex algorithm, however, may compromise the desired integrity. In this paper we propose a lightweight encryption algorithm named as Secure IoT (SIT). It is a 64-bit block cipher and requires 64-bit key to encrypt the data. The architecture of the algorithm is a mixture of feistel and a uniform substitution-permutation network. Simulations result shows the algorithm provides substantial security in just five encryption rounds. The hardware implementation of the algorithm is done on a low cost 8-bit micro-controller and the results of code size, memory utilization and encryption/decryption execution cycles are compared with benchmark encryption algorithms. The MATLAB code for relevant simulations is available online at Read More
  • We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality. Read More
  • In this paper, we study the evolution of asymptotically AdS initial data for the spherically symmetric Einstein--massless Vlasov system for $\Lambda<0$, with reflecting boundary conditions imposed on timelike infinity $\mathcal{I}$, in the case when the Vlasov field is supported only on radial geodesics. This system is equivalent to the spherically symmetric Einstein--null dust system, allowing for both ingoing and outgoing dust. In general, solutions to this system break down in finite time (independent of the size of the initial data); we highlight this fact by showing that, at the first point where the ingoing dust reaches the axis of symmetry, solutions become $C^{0}$ inextendible, although the spacetime metric remains regular up to that point. One way to overcome this trivial obstacle to well-posedness is to place an inner mirror on a timelike hypersurface of the form $\{r=r_{0}\}$, $r_{0}>0$, and study the evolution on the exterior domain $\{r\ge r_{0}\}$. In this setting, we prove the existence and uniqueness of maximal developments for general smooth and asymptotically AdS initial data sets, and study the basic geometric properties of these developments. Furthermore, we establish the well-posedness and Cauchy stabilty of solutions with respect to a rough initial data norm, measuring the concentration of energy at scales proportional to the mirror radius $r_{0}$. The above well-posedness and Cauchy stability estimates are used in our companion paper for the proof of the AdS instability conjecture for the Einstein--null dust system. However, the results of the present paper might also be of independent interest. Read More
  • In order to better understand the effect of the electron-phonon interaction on the volume collapse transition of Cerium, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling can enhance the volume collapse, which is consistent with experiments. Although we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling. Read More
  • We study the strong duality of non-convex matrix factorization: we show under certain dual conditions, non-convex matrix factorization and its dual have the same optimum. This has been well understood for convex optimization, but little was known for matrix factorization. We formalize the strong duality of matrix factorization through a novel analytical framework, and show that the duality gap is zero for a wide class of matrix factorization problems. Although matrix factorization problems are hard to solve in full generality, under certain conditions the optimal solution of the non-convex program is the same as its bi-dual, and we can achieve global optimality of the non-convex program by solving its bi-dual. We apply our framework to matrix completion and robust Principal Component Analysis (PCA). While a long line of work has studied these problems, for basic problems in this area such as matrix completion, the information-theoretically optimal sample complexity was not known, and the sample complexity bounds if one also requires computational efficiency are even larger. In this work, we show that exact recoverability and strong duality hold with optimal sample complexity guarantees for matrix completion, and nearly-optimal guarantees for exact recoverability of robust PCA. For matrix completion, under the standard incoherence assumption that the underlying rank-$r$ matrix $X^*\in \mathbb{R}^{n\times n}$ with skinny SVD $U \Sigma V^T$ has $\max\{\|U^Te_i\|_2^2, \|V^Te_i\|_2^2\} \leq \frac{\mu r}{n}$ for all $i$, to the best of our knowledge we give (1) the first non-efficient algorithm achieving the optimal $O(\mu n r \log n)$ sample complexity, and (2) the first efficient algorithm achieving $O(\kappa^2\mu n r \log n)$ sample complexity, which matches the known $\Omega(\mu n r \log n)$ information-theoretic lower bound for constant condition number $\kappa$. Read More
  • In 2006, Dafermos and Holzegel formulated the so-called AdS instability conjecture, stating that there exist arbitrarily small perturbations to AdS initial data which, under evolution by the Einstein vacuum equations for $\Lambda<0$ with reflecting boundary conditions on conformal infinity, lead to the formation of black holes. The numerical study of this conjecture in the simpler setting of the spherically symmetric Einstein--scalar field system was initiated by Bizon and Rostworowski, followed by a vast number of numerical and heuristic works by several authors. In this paper, we provide the first rigorous proof of the AdS instability conjecture in the simplest possible setting, namely for the spherically symmetric Einstein--massless Vlasov system, in the case when the Vlasov field is moreover supported only on radial geodesics. This system is equivalent to the Einstein--null dust system, allowing for both ingoing and outgoing dust. In order to overcome the break down of this system occuring once the null dust reaches the centre $r=0$, we place an inner mirror at $r=r_{0}>0$ and study the evolution of this system on the exterior domain $\{r\ge r_{0}\}$. The structure of the maximal development and the Cauchy stability properties of general initial data in this setting are studied in our companion paper. The statement of the main theorem is as follows: We construct a family of mirror radii $r_{0\epsilon}>0$ and initial data $\mathcal{S}_{\epsilon}$, $\epsilon\in(0,1]$, converging to the AdS initial data in a suitable norm, such that, for any $\epsilon>0$, the maximal development $(\mathcal{M}_{\epsilon},g_{\epsilon})$ of $\mathcal{S}_{\epsilon}$ contains a black hole region. Our proof is based on purely physical space arguments. Read More