On the noncommutative standard model

We propose a pedestrian review of the noncommutative standard model in its present state.Comment: dedicated to Alain Connes on the occasion of his 60th birthda

Stability of domain walls in models with asymmetric potentials

We study the evolution of cosmological domain walls in models with asymmetric potentials. Our research goes beyond the standard case of spontaneous breaking of an approximate symmetry. When the symmetry is explicitly broken the potential exhibits nearly degenerate minima which can lead to creation of a metastable network of domain walls. The time after which the network will decay depends on the difference of values of the potential in minima, its asymmetry around the maximum separating minima and the bias of the initial distribution of the field. Effect of asymmetry around the maximum separating minima is novel one that we study with a new type of potential. Using numerical lattice simulations we determine relative importance of these factors on decay time of networks for generic potentials. We find that even very small departures from the symmetric initial distribution case lead to rapid decay of the domain wall network. As a result creation of a long lasting network capable of producing observable gravitational wave signals is much more difficult than previously thought. On the other hand details of the shape of the potential turn out to be much less important than was expected and the evolution of network from symmetric distribution is controlled by the difference of values of the potential in the minima

Finding the Standard Model of Particle Physics, A Combinatorial Problem

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang-Mills-Higgs models

Mixture of Tokens: Efficient LLMs through Cross-Example Aggregation

Despite the promise of Mixture of Experts (MoE) models in increasing parameter counts of Transformer models while maintaining training and inference costs, their application carries notable drawbacks. The key strategy of these models is to, for each processed token, activate at most a few experts - subsets of an extensive feed-forward layer. But this approach is not without its challenges. The operation of matching experts and tokens is discrete, which makes MoE models prone to issues like training instability and uneven expert utilization. Existing techniques designed to address these concerns, such as auxiliary losses or balance-aware matching, result either in lower model performance or are more difficult to train. In response to these issues, we propose Mixture of Tokens, a fully-differentiable model that retains the benefits of MoE architectures while avoiding the aforementioned difficulties. Rather than routing tokens to experts, this approach mixes tokens from different examples prior to feeding them to experts, enabling the model to learn from all token-expert combinations. Importantly, this mixing can be disabled to avoid mixing of different sequences during inference. Crucially, this method is fully compatible with both masked and causal Large Language Model training and inference

Seesaw and noncommutative geometry

The 1-loop corrections to the seesaw mechanism in the noncommutative standard model are computed. Other consequences of the Lorentzian signature in the inner space are summarised.Comment: Dedicated to Alain Connes on the occasion of his 60th birthda

The correlation of protein peroxidation with morphological changes in experimental oestradiol-induced carcinogenesis

Oestradiol-induced male Syrian hamster carcinogenesis is a well-known experimental model of human cancer of the breast, ovary and uterus. The pathomechanism postulated in this model is 4-hydroxylation of oestradiol and further free radical formation. The same process is suspected in human breast cancer. Dynamic changes in protein peroxidation were reported during the tumour induction. In this paper we try to correlate the protein peroxidation markers with the histopathological progression of the changes. The biochemical and histopathological evaluations were performed after 1, 3, 6 and 9 months of the hormone exposition. Significant protein peroxidation was observed as soon as after 1 month and increased further until the 6th month. After 9 months however, it was not significantly different from the control. The discrete histopathological changes after 1 month, progressed into tubular and interstitial hyperplasias after 3 and 6 months. After 9 months several dysplastic areas, sometimes with features of carcinoma in situ, were observed. The severe 9-month histopathological changes did not correlate with the protein peroxidation

Prenatal ultrasonographic diagnosis of congenital epulis – two case reports and literature review

Abstract The following work presents prenatal ultrasonographic examination of two rare fetal cases of epulis, among 13 792 fetuses referred to our unit due to suspected fetal anomalies by obstetricians (estimated prevalence 1/7000 among fetuses with different anomalies). Sonographic differential diagnosis, value of fetal nasal amniotic fluid flow assessment by color Doppler and the probability of EXIT procedure have been described