Critical-point anomalies in doped CeRhIn5

The heavy-fermion compound CeRhIn$_5$ can be tuned through a quantum critical point, when In is partially replaced by Sn. This way additional charge carriers are introduced and the antiferromagnetic order is gradually suppressed to zero temperature. Here we investigate the temperature-dependent optical properties of CeRh(In$_{1-x}$Sn$_x$)$_5$ single crystals for $x = 4.4\%$, $6.9\%$ and $9.8\%$. With increasing Sn concentration the infrared conductivity reveals a clear enhancement of the $c$-$f$ hybridization strength. At low temperatures we observed a non-Fermi-liquid behavior in the frequency dependence of the scattering rate and effective mass in all three compounds. In addition, below a characteristic temperature $T^* \approx 10$ K, the temperature dependent resistivity $\rho(T)$ follows a $\log T$ behavior, typical for a non-Fermi liquid. The temperature-dependent magnetization also exhibits anomalous behavior below $T^*$. Our investigation reveal that below $T^*$ the system shows a pronounced non-Fermi-liquid behavior and $T^*$ monotonically increases as the quantum critical point is approached

Novel methods for anomaly detection

Anomaly detection is of increasing importance in the data rich world of today. It can be applied to a broad range of challenges ranging from fault detection to fraud prevention and cyber-security. Many of these application require algorithms which are very scalable, as well as accurate, due to large data volumes and/or limited computational resources. This thesis contributes three novel approaches to the field of anomaly detection. The first contribution, Collective And Point Anomalies (CAPA) detects and distinguishes between both collective and point anomalies in linear time. The second contribution, MultiVariate Collective And Point Anomalies (MVCAPA) extends CAPA to the multivariate setting. The third contribution is a novel particle based kalman filter which detects and distinguished between additive outliers and innovative outliers

Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux

We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribute to the cancellation of the four-dimensional anomaly and the generation of a vector boson mass via the Stueckelberg mechanism. An orthogonal linear combination of the axions remains massless and couples to the gauge field in the standard way. Furthermore, we construct convenient expressions for the wave functions of the zero modes and relate their multiplicity and behavior at the fixed points to the bulk flux quanta and the Wilson lines.Comment: 30 pages, 4 figures, 1 table, clarifying remarks adde

TeV scale 5D SU(3)WSU(3)_W unification and the fixed point anomaly cancellation with chiral split multiplets

A possibility of 5D gauge unification of $SU(2)_L \times U(1)_Y$ in $SU(3)_W$ is examined. The orbifold compactification allows fixed points where $SU(2)_L\times U(1)_Y$ representations can be assigned. We present a few possibilities which give long proton lifetime, top-bottom mass hierarchy from geometry, and reasonable neutrino masses. In general, these {\it chiral models} can lead to fixed point anomalies. We can show easily, due to the simplicity of the model, that these anomalies are cancelled by the relevant Chern-Simons terms for all the models we consider. It is also shown that the fixed point U(1)--graviton--graviton anomaly cancels without the help from the Chern-Simons term. Hence, we conjecture that the fixed point anomalies can be cancelled if the effective 4D theory is made anomaly free by locating chiral fermions at the fixed points.Comment: LaTeX file of 19 pages with 1 figur

Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstruction

Time series anomaly detection is challenging due to the complexity and variety of patterns that can occur. One major difficulty arises from modeling time-dependent relationships to find contextual anomalies while maintaining detection accuracy for point anomalies. In this paper, we propose a framework for unsupervised time series anomaly detection that utilizes point-based and sequence-based reconstruction models. The point-based model attempts to quantify point anomalies, and the sequence-based model attempts to quantify both point and contextual anomalies. Under the formulation that the observed time point is a two-stage deviated value from a nominal time point, we introduce a nominality score calculated from the ratio of a combined value of the reconstruction errors. We derive an induced anomaly score by further integrating the nominality score and anomaly score, then theoretically prove the superiority of the induced anomaly score over the original anomaly score under certain conditions. Extensive studies conducted on several public datasets show that the proposed framework outperforms most state-of-the-art baselines for time series anomaly detection.Comment: NeurIPS 2023 (https://neurips.cc/virtual/2023/poster/70582

Critical Point Anomalies Include Expansion Shock Waves

From first-principle fluid dynamics, complemented by a rigorous state equation accounting for critical anomalies, we discovered that expansion shock waves may occur in the vicinity of the liquid-vapor critical point in the two-phase region. Due to universality of near-critical thermodynamics, the result is valid for any common pure fluid in which molecular interactions are only short-range, namely, for so-called 3-dimensional Ising-like systems, and under the assumption of thermodynamic equilibrium. In addition to rarefaction shock waves, diverse non-classical effects are admissible, including composite compressive shock-fan-shock waves, due to the change of sign of the fundamental derivative of gasdynamics