Subspace clustering of dimensionality-reduced data

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from "undersampling" due to complexity and speed constraints on the acquisition device. More pertinently, even if one has access to the high-dimensional data set it is often desirable to first project the data points into a lower-dimensional space and to perform the clustering task there; this reduces storage requirements and computational cost. The purpose of this paper is to quantify the impact of dimensionality-reduction through random projection on the performance of the sparse subspace clustering (SSC) and the thresholding based subspace clustering (TSC) algorithms. We find that for both algorithms dimensionality reduction down to the order of the subspace dimensions is possible without incurring significant performance degradation. The mathematical engine behind our theorems is a result quantifying how the affinities between subspaces change under random dimensionality reducing projections.Comment: ISIT 201

Coefficient of Restitution as a Fluctuating Quantity

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, $p(\epsilon)$, is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.Comment: 4 pages, 4 figure

Energy Dissipation in Driven Granular Matter in the Absence of Gravity

We experimentally investigate the energy dissipation rate in sinusoidally driven boxes which are partly filled by granular material under conditions of weightlessness. We identify two different modes of granular dynamics, depending on the amplitude of driving, $A$. For intense forcing, A>A_0, the material is found in the collect-and-collide regime where the center of mass of the granulate moves synchronously with the driven container while for weak forcing, A<A_0, the granular material exhibits gas-like behavior. Both regimes correspond to different dissipation mechanisms, leading to different scaling with amplitude and frequency of the excitation and with the mass of the granulate. For the collect-and-collide regime, we explain the dependence on frequency and amplitude of the excitation by means of an effective one-particle model. For both regimes, the results may be collapsed to a single curve characterizing the physics of granular dampers.Comment: 5 pages, 3 figure

Cichlids do not adjust reproductive skew to the availability of independent breeding options

Helpers in cooperatively breeding species forego all or part of their reproduction when remaining at home and assisting breeders to raise offspring. Different models of reproductive skew generate alternative predictions about the share of reproduction unrelated subordinates will get depending on the degree of ecological constraints. Concession models predict a larger share when independent breeding options are good, whereas restraint and tug-of-war models predict no effects on reproductive skew. We tested these predictions by determining the share of reproduction by unrelated male and female helpers in the Lake Tanganyika cichlid Neolamprologus pulcher depending on experimentally manipulated possibilities for helper dispersal and independent breeding and depending on helper size and sex. We created 32 breeding groups in the laboratory, consisting of two breeders and two helpers each, where only the helpers had access to a nearby dispersal compartment with (treatment) or without (control) breeding substrate, using a repeated measures design. We determined the paternity and maternity of 1185 offspring from 47 broods using five to nine DNA microsatellite loci and found that: (1) helpers participated in reproduction equally across the treatments, (2) large male helpers were significantly more likely to reproduce than small helpers, and (3) male helpers engaged in significantly more reproduction than female helpers. Interestingly, in four broods, extragroup helper males had fertilized part of the brood. No helper evictions from the group after helper reproduction were observed. Our results suggest that tug-of-war models based on competition over reproduction within groups describe best the reproductive skew observed in our study system. Female breeders produced larger clutches in the treatment compared to the control situation when the large helpers were males. This suggests that male breeder-male helper reproductive conflicts may be alleviated by females producing larger clutches with helpers aroun

Modeling and Reasoning over Distributed Systems using Aspect-Oriented Graph Grammars

Aspect-orientation is a relatively new paradigm that introduces abstractions to modularize the implementation of system-wide policies. It is based on a composition operation, called aspect weaving, that implicitly modifies a base system by performing related changes within the system modules. Aspect-oriented graph grammars (AOGG) extend the classic graph grammar formalism by defining aspects as sets of rule-based modifications over a base graph grammar. Despite the advantages of aspect-oriented concepts regarding modularity, the implicit nature of the aspect weaving operation may also introduce issues when reasoning about the system behavior. Since in AOGGs aspect weaving is characterized by means of rule-based rewriting, we can overcome these problems by using known analysis techniques from the graph transformation literature to study aspect composition. In this paper, we present a case study of a distributed client-server system with global policies, modeled as an aspect-oriented graph grammar, and discuss how to use the AGG tool to identify potential conflicts in aspect weaving

K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI), where acquisition of high-resolution fully sampled k-space data is impractical. We introduce a novel mathematical framework, dubbed k-band, that enables training DL models using only partial, limited-resolution k-space data. Specifically, we introduce training with stochastic gradient descent (SGD) over k-space subsets. In each training iteration, rather than using the fully sampled k-space for computing gradients, we use only a small k-space portion. This concept is compatible with different sampling strategies; here we demonstrate the method for k-space "bands", which have limited resolution in one dimension and can hence be acquired rapidly. We prove analytically that our method stochastically approximates the gradients computed in a fully-supervised setup, when two simple conditions are met: (i) the limited-resolution axis is chosen randomly-uniformly for every new scan, hence k-space is fully covered across the entire training set, and (ii) the loss function is weighed with a mask, derived here analytically, which facilitates accurate reconstruction of high-resolution details. Numerical experiments with raw MRI data indicate that k-band outperforms two other methods trained on limited-resolution data and performs comparably to state-of-the-art (SoTA) methods trained on high-resolution data. k-band hence obtains SoTA performance, with the advantage of training using only limited-resolution data. This work hence introduces a practical, easy-to-implement, self-supervised training framework, which involves fast acquisition and self-supervised reconstruction and offers theoretical guarantees

Rapid At‐Line AAVX Affinity HPLC: Enabling Process Analytical Technology for Bioprocess Development of Adeno‐Associated Virus Vectors

Recombinant adeno-associated virus (rAAV) vectors have emerged as a new class of therapeutic modal with the promise to treat or even cure hereditary and acquired diseases, but their consistent and efficient production remains challenging. To address these inadequacies, the implementation of process analytical technology (PAT) principles for the development of rAAV-based gene therapies holds the prospect of promoting greater product and process understanding. However, a substantial lack of suitable analytical tools during both upstream and downstream processing (DSP) hinders the ability to fully realize the potential of PAT for rAAVs. To fill this gap, our recently described AAVX affinity-based high-performance liquid chromatography (HPLC) method was assessed as an at-line PAT tool to determine the capsid titer and the percentage of filled capsids at various stages of the production process. Leveraging the fast and robust provision of these parameters, even for challenging samples, the benefits of this approach for improved process monitoring and control were demonstrated for samples generated both during fermentation and DSP. Given the versatility of our developed analytical method for different rAAV serotype and payload combinations, we eventually highlight its expansive opportunities to streamline process development and therefore contributing to high-quality and cost-efficient production of rAAV-based gene therapies