Poincar\'e invariance in NRQCD and pNRQCD revisited

We investigate how fields transform under the Poincar\'e group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed terms. By requiring invariance of the action under these transformations, nontrivial relations between Wilson coefficients for both nonrelativistic QCD and potential nonrelativistic QCD are derived. We show explicitly how the Poincar\'e algebra is satisfied, and how this gives complementary information on the Wilson coefficients. We also briefly discuss the implications of our results, as well as the possibility of applying this method to other types of effective field theories.Comment: 56 page

Universality classes of interaction structures for NK fitness landscapes

Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of $L$ binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $k \le L$ loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of $L$, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large $k$. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in $L$ for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.Comment: 61 pages, 9 figure

On the number of limit cycles in asymmetric neural networks

The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience. In this work, we investigate how the structure of recurrent connectivity influences the ability of a network to have storable patterns and in particular limit cycles, by modeling a recurrent neural network with McCulloch-Pitts neurons as a content-addressable memory system. A key role in such models is played by the connectivity matrix, which, for neural networks, corresponds to a schematic representation of the "connectome": the set of chemical synapses and electrical junctions among neurons. The shape of the recurrent connectivity matrix plays a crucial role in the process of storing memories. This relation has already been exposed by the work of Tanaka and Edwards, which presents a theoretical approach to evaluate the mean number of fixed points in a fully connected model at thermodynamic limit. Interestingly, further studies on the same kind of model but with a finite number of nodes have shown how the symmetry parameter influences the types of attractors featured in the system. Our study extends the work of Tanaka and Edwards by providing a theoretical evaluation of the mean number of attractors of any given length $L$ for different degrees of symmetry in the connectivity matrices.Comment: 35 pages, 12 figure

Mutation supply and the repeatability of selection for antibiotic resistance

Whether evolution can be predicted is a key question in evolutionary biology. Here we set out to better understand the repeatability of evolution. We explored experimentally the effect of mutation supply and the strength of selective pressure on the repeatability of selection from standing genetic variation. Different sizes of mutant libraries of an antibiotic resistance gene, TEM-1 $\beta$-lactamase in Escherichia coli, were subjected to different antibiotic concentrations. We determined whether populations went extinct or survived, and sequenced the TEM gene of the surviving populations. The distribution of mutations per allele in our mutant libraries- generated by error-prone PCR- followed a Poisson distribution. Extinction patterns could be explained by a simple stochastic model that assumed the sampling of beneficial mutations was key for survival. In most surviving populations, alleles containing at least one known large-effect beneficial mutation were present. These genotype data also support a model which only invokes sampling effects to describe the occurrence of alleles containing large-effect driver mutations. Hence, evolution is largely predictable given cursory knowledge of mutational fitness effects, the mutation rate and population size. There were no clear trends in the repeatability of selected mutants when we considered all mutations present. However, when only known large-effect mutations were considered, the outcome of selection is less repeatable for large libraries, in contrast to expectations. Furthermore, we show experimentally that alleles carrying multiple mutations selected from large libraries confer higher resistance levels relative to alleles with only a known large-effect mutation, suggesting that the scarcity of high-resistance alleles carrying multiple mutations may contribute to the decrease in repeatability at large library sizes.Comment: 31pages, 9 figure

On the number of limit cycles in diluted neural networks

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus.Comment: 10 pages, 11 figure

Learning to Unlearn: Instance-wise Unlearning for Pre-trained Classifiers

Since the recent advent of regulations for data protection (e.g., the General Data Protection Regulation), there has been increasing demand in deleting information learned from sensitive data in pre-trained models without retraining from scratch. The inherent vulnerability of neural networks towards adversarial attacks and unfairness also calls for a robust method to remove or correct information in an instance-wise fashion, while retaining the predictive performance across remaining data. To this end, we consider instance-wise unlearning, of which the goal is to delete information on a set of instances from a pre-trained model, by either misclassifying each instance away from its original prediction or relabeling the instance to a different label. We also propose two methods that reduce forgetting on the remaining data: 1) utilizing adversarial examples to overcome forgetting at the representation-level and 2) leveraging weight importance metrics to pinpoint network parameters guilty of propagating unwanted information. Both methods only require the pre-trained model and data instances to forget, allowing painless application to real-life settings where the entire training set is unavailable. Through extensive experimentation on various image classification benchmarks, we show that our approach effectively preserves knowledge of remaining data while unlearning given instances in both single-task and continual unlearning scenarios.Comment: AAAI 2024 camera ready versio

Inflammation-induced Id2 promotes plasticity in regulatory T cells

T(H)17 cells originating from regulatory T (T-reg) cells upon loss of the T-reg-specific transcription factor Foxp3 accumulate in sites of inflammation and aggravate autoimmune diseases. Whether an active mechanism drives the generation of these pathogenic 'ex-Foxp3 T(H)17' cells, remains unclear. Here we show that pro-inflammatory cytokines enhance the expression of transcription regulator Id2, which mediates cellular plasticity of T-reg into 'ex-Foxp3' T(H)17 cells. Expression of Id2 in in vitro differentiated iT(reg) cells reduces the expression of Foxp3 by sequestration of the transcription activator E2A, leading to the induction of T(H)17-related cytokines. T-reg-specific ectopic expression of Id2 in mice significantly reduces the T-reg compartment and causes immune dysregulation. Cellular fate-mapping experiments reveal enhanced T-reg plasticity compared to wild-type, resulting in exacerbated experimental autoimmune encephalomyelitis pathogenesis or enhanced anti-tumor immunity. Our findings suggest that controlling Id2 expression may provide a novel approach for effective T-reg cell immunotherapies for both autoimmunity and cancer.11sciescopu