On Finite 4D Quantum Field Theory in Non-Commutative Geometry

The truncated 4-dimensional sphere $S^4$ and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the finite number of degrees of freedom. The usual field theory UV-divergences are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove

Generic Black-Box End-to-End Attack Against State of the Art API Call Based Malware Classifiers

In this paper, we present a black-box attack against API call based machine learning malware classifiers, focusing on generating adversarial sequences combining API calls and static features (e.g., printable strings) that will be misclassified by the classifier without affecting the malware functionality. We show that this attack is effective against many classifiers due to the transferability principle between RNN variants, feed forward DNNs, and traditional machine learning classifiers such as SVM. We also implement GADGET, a software framework to convert any malware binary to a binary undetected by malware classifiers, using the proposed attack, without access to the malware source code.Comment: Accepted as a conference paper at RAID 201

Spin dependent fragmentation function at Belle

The measurement of the so far unknown chiral-odd quark transverse spin distribution in either semi-inclusive DIS (SIDIS) or inclusive measurements in pp collisions at RHIC has an additional chiral-odd fragmentation function appearing in the cross section. These chiral-odd fragmentation functions (FF) can for example be the so-called Collins FF or the Interference FF. HERMES has given a first hint that these FFs are nonzero, however in order to measure the transversity one needs these FFs to be precisely known. We have used 29.0 fb$^{-1}$ of data collected by the Belle experiment at the KEKB $e^+e^-$ collider to measure azimuthal asymmetries for different charge combinations of pion pairs and thus access the Collins FF.Comment: Results presented at the DIS 2006 conference in Tsukuba, Japa

Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator

It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$ axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form $\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where $a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$ but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion $\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .Comment: 26 pages, latex fil

Regularization of 2d supersymmetric Yang-Mills theory via non commutative geometry

The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on supersphere [14]. This paper is a generalization of this latter work to more general gauge groups

J-Class Abelian Semigroups of Matrices on C^n and Hypercyclicity

We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 2 an abelian semigroup G of GL(n;C) generated by n + 1 diagonal matrices which is locally hypercyclic but not hypercyclic and such that JG(e_k) = C^n for every k = 1; : : : ; n, where (e_1; : : : ; e_n) is the canonical basis of C^n. This gives a negative answer to a question raised by Costakis and Manoussos.Comment: 10 page

A New Noncommutative Product on the Fuzzy Two-Sphere Corresponding to the Unitary Representation of SU(2) and the Seiberg-Witten Map

We obtain a new explicit expression for the noncommutative (star) product on the fuzzy two-sphere which yields a unitary representation. This is done by constructing a star product, $\star_{\lambda}$, for an arbitrary representation of SU(2) which depends on a continuous parameter $\lambda$ and searching for the values of $\lambda$ which give unitary representations. We will find two series of values: $\lambda = \lambda^{(A)}_j=1/(2j)$ and $\lambda=\lambda^{(B)}_j =-1/(2j+2)$, where j is the spin of the representation of SU(2). At $\lambda = \lambda^{(A)}_j$ the new star product $\star_{\lambda}$ has poles. To avoid the singularity the functions on the sphere must be spherical harmonics of order $\ell \leq 2j$ and then $\star_{\lambda}$ reduces to the star product $\star$ obtained by Preusnajder. The star product at $\lambda=\lambda^{(B)}_j$, to be denoted by $\bullet$, is new. In this case the functions on the fuzzy sphere do not need to be spherical harmonics of order $\ell \leq 2j$. Because in this case there is no cutoff on the order of spherical harmonics, the degrees of freedom of the gauge fields on the fuzzy sphere coincide with those on the commutative sphere. Therefore, although the field theory on the fuzzy sphere is a system with finite degrees of freedom, we can expect the existence of the Seiberg-Witten map between the noncommutative and commutative descriptions of the gauge theory on the sphere. We will derive the first few terms of the Seiberg-Witten map for the U(1) gauge theory on the fuzzy sphere by using power expansion around the commutative point $\lambda=0$.Comment: 15 pages, typos corrected, references added, a note adde

The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4

We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and the divergent contributions corrected accordingly. As a result the model turns out to be asymptotically fre