arXiv subjects

Michael Weiss

Publications and source records attributed to Michael Weiss.

28 records · Page 2Linked to original sources

arXiv2019

Misbehaviour Prediction for Autonomous Driving Systems

Deep Neural Networks (DNNs) are the core component of modern autonomous driving systems. To date, it is still unrealistic that a DNN will generalize correctly in all driving conditions. Current testing techniques consist of offline solutions that identify adversarial or corner cases for improving the training phase, and little has been done for enabling online healing of DNN-based vehicles. In this paper, we address the problem of estimating the confidence of DNNs in response to unexpected execution contexts with the purpose of predicting potential safety-critical misbehaviours such as out of bound episodes or collisions. Our approach SelfOracle is based on a novel concept of self-assessment oracle, which monitors the DNN confidence at runtime, to predict unsupported driving scenarios in advance. SelfOracle uses autoencoder and time-series-based anomaly detection to reconstruct the driving scenarios seen by the car, and determine the confidence boundary of normal/unsupported conditions. In our empirical assessment, we evaluated the effectiveness of different variants of SelfOracle at predicting injected anomalous driving contexts, using DNN models and simulation environment from Udacity. Results show that, overall, SelfOracle can predict 77% misbehaviours, up to 6 seconds in advance, outperforming the online input validation approach of DeepRoad by a factor almost equal to 3.

eess.SP↗

arXiv2015

On the Distribution of Rational Squares

Let $a$ be a positive integer, and let $σ(a)$ denote the least natural number $s$ such that an integer square lies between $s^2 a$ and $s^2 (a+1)$; let $τ_s(a)$ denote the number of such integer squares. The function $σ(a)$ and the sequence $(τ_s(a))_{s \in \mathbb{Z}^+}$ are studied, and are observed to exhibit surprisingly chaotic behavior. Upper- and lower-bounds for $σ(a)$ are derived, as are criteria for when they are sharp.

math.NT↗

arXiv2010

On the algebraic $L$-theory of $Δ$-sets

The algebraic $L$-groups $L_*(\A,X)$ are defined for an additive category $\A$ with chain duality and a $Δ$-set $X$, and identified with the generalized homology groups $H_*(X;\LL_{\bullet}(\A))$ of $X$ with coefficients in the algebraic $L$-spectrum $\LL_{\bullet}(\A)$. Previously such groups had only been defined for simplicial complexes $X$.

math.AT↗

arXiv2010

The homotopy type of the cobordism category

The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.

math.AT↗

arXiv2010

On the construction and topological invariance of the Pontryagin classes

We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with fiber R^n. This amounts to an alternative proof of Novikov's theorem on the topological invariance of the rational Pontryagin classes of vector bundles. Transversality arguments and torus tricks are avoided.

math.AT↗

arXiv2009

2D cellular automata: dynamics and undecidability

In this paper we introduce the notion of quasi-expansivity for 2D CA and we show that it shares many properties with expansivity (that holds only for 1D CA). Similarly, we introduce the notions of quasi-sensitivity and prove that the classical dichotomy theorem holds in this new setting. Moreover, we show a tight relation between closingness and openness for 2D CA. Finally, the undecidability of closingness property for 2D CA is proved.

cs.FL↗

arXiv2007

The block structure spaces of real projective spaces and orthogonal calculus of functors II

For a finite dimensional real vector space V with inner product, let F(V) be the block structure space, in the sense of surgery theory, of the projective space of V. Continuing a program launched in part I, we investigate F as a functor on vector spaces with inner product, relying on functor calculus ideas. It was shown in part I that F agrees with its first Taylor approximation T_1 F (which is a polynomial functor of degree 1) on vector spaces V with dim(V) > 5. To convert this theorem into a functorial homotopy-theoretic description of F(V), one needs to know in addition what T_1 F(V) is when V=0. Here we show that T_1 F(0) is the standard L-theory space associated with the group Z/2, except for a deviation in π_0. The main corollary is a functorial two-stage decomposition of F(V) for dim(V) > 5 which has the L-theory of the group Z/2 as one layer, and a form of unreduced homology of RP (V) with coefficients in the L-theory of the trivial group as the other layer. (Except for dimension shifts, these are also the layers in the traditional Sullivan-Wall-Quinn-Ranicki decomposition of F(V). But the dimension shifts are serious and the SWQR decomposition of F(V) is not functorial in V.) Because of the functoriality, our analysis of F(V) remains meaningful and valid when V=R^\infty.

math.AT↗

arXiv1999

Embeddings from the point of view of immersion theory: Part II

Let M and N be smooth manifolds. For an open V of M let emb(V,N) be the space of embeddings from V to N. By results of Goodwillie and Goodwillie-Klein, the cofunctor V |--> emb(V,N) is analytic if dim(N)-dim(M) > 2. We deduce that its Taylor series converges to it. For details about the Taylor series, see Part I.

math.GT↗

arXiv1999

Embeddings from the point of view of immersion theory: Part I

Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |--> emb(V,N) from the poset O of open subsets of M to spaces. We therefore abstract some of the properties of this cofunctor, and develop a suitable calculus of such cofunctors, Goodwillie style, with Taylor series and so on. The terms of the Taylor series for the cofunctor V |--> emb(V,N) are explicitly determined. In a sequel to this paper, we introduce the concept of an analytic cofunctor from O to spaces, and show that the Taylor series of an analytic cofunctor F converges to F. Deep excision theorems due to Goodwillie and Goodwillie-Klein imply that the cofunctor V |--> emb(V,N) is analytic when dim(N)-dim(M) > 2.

math.GT↗

arXiv1997

Dry Friction in the Frenkel-Kontorova-Tomlinson Model: Dynamical Properties

Wearless friction is investigated in a simple mechanical model called Frenkel-Kontorova-Tomlinson model. We have introduced this model in [Phys. Rev. B, Vol. 53, 7539 (1996)] where the static friction has already been considered. Here the model is treated for constant sliding speed. The kinetic friction is calculated numerically as well as analytically. As a function of the sliding velocity it shows many structures which can be understood by varies kinds of phonon resonances (normal, superharmonic and parametric) caused by the so-called "washboard wave". For increasing interaction strength the regular motion becomes chaotic (fluid-sliding state). The fluid sliding state is mainly determined by the density of decay channels of m washboard waves into n phonons. We also find strong bistabilities and coherent motions with superimposed dark envelope solitons which interact nondestructively.

cond-mat.stat-mech↗