Regular subgroups with large intersection

In this paper we study the relationships between the elementary abelian regular subgroups and the Sylow $2$-subgroups of their normalisers in the symmetric group $\mathrm{Sym}(\mathbb{F}_2^n)$, in view of the interest that they have recently raised for their applications in symmetric cryptography

A modular idealizer chain and unrefinability of partitions with repeated parts

Recently Aragona et al. have introduced a chain of normalizers in a Sylow 2-subgroup of Sym(2^n), starting from an elementary abelian regular subgroup. They have shown that the indices of consecutive groups in the chain depend on the number of partitions into distinct parts and have given a description, by means of rigid commutators, of the first n-2 terms in the chain. Moreover, they proved that the (n-1)-th term of the chain is described by means of rigid commutators corresponding to unrefinable partitions into distinct parts. Although the mentioned chain can be defined in a Sylow p-subgroup of Sym(p^n), for p > 2 computing the chain of normalizers becomes a challenging task, in the absence of a suitable notion of rigid commutators. This problem is addressed here from an alternative point of view. We propose a more general framework for the normalizer chain, defining a chain of idealizers in a Lie ring over Z_m whose elements are represented by integer partitions. We show how the corresponding idealizers are generated by subsets of partitions into at most m-1 parts and we conjecture that the idealizer chain grows as the normalizer chain in the symmetric group. As an evidence of this, we establish a correspondence between the two constructions in the case m=2

Identification of new HIV-1 Gag-specific cytotoxic T lymphocyte responses in BALB/c mice

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A Chain of Normalizers in the Sylow 22-subgroups of the symmetric group on 2n2^n letters

On the basis of an initial interest in symmetric cryptography, in the present work we study a chain of subgroups. Starting from a Sylow $2$-subgroup of AGL(2,n), each term of the chain is defined as the normalizer of the previous one in the symmetric group on $2^n$ letters. Partial results and computational experiments lead us to conjecture that, for large values of $n$, the index of a normalizer in the consecutive one does not depend on $n$. Indeed, there is a strong evidence that the sequence of the logarithms of such indices is the one of the partial sums of the numbers of partitions into at least two distinct parts

The Enigma of Tripeptidyl-Peptidase II: Dual Roles in Housekeeping and Stress

The tripeptidyl-peptidase II complex consists of repeated 138 kDa subunits, assembled into two twisted strands that form a high molecular weight complex (>5 MDa). TPPII, like many other cytosolic peptidases, plays a role in the ubiquitin-proteasome pathway downstream of the proteasome as well as in the production and destruction of MHC class I antigens and degradation of neuropeptides. Tripeptidyl-peptidase II activity is increased in cells with an increased demand for protein degradation, but whether degradation of cytosolic peptides is the only cell biological role for TPPII has remained unclear. Recent data indicated that TPPII translocates into the nucleus to control DNA damage responses in malignant cells, supporting that cytosolic “housekeeping peptidases” may have additional roles in cell biology, besides their contribution to protein turnover. Overall, TPPII has an emerging importance in several cancer-related fields, such as metabolism, cell death control, and control of genome integrity; roles that are not understood in detail. The present paper reviews the cell biology of TPPII and discusses distinct roles for TPPII in the nucleus and cytosol

Rigid commutators and a normalizer chain

The novel notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetric group on 2^n letters. The terms of this sequence are proved to be those of the partial sums of the partitions of an integer into at least two distinct parts, that relates to a famous Euler's partition theorem

Epitope-dependent Selection of Highly Restricted or Diverse T Cell Receptor Repertoires in Response to Persistent Infection by Epstein-Barr Virus

The T cell receptor (TCR) repertoires of cytotoxic responses to the immunodominant and subdominant HLA A11–restricted epitopes in the Epstein-Barr virus (EBV) nuclear antigen-4 were investigated in four healthy virus carriers. The response to the subdominant epitope (EBNA4 399-408, designated AVF) was highly restricted with conserved Vβ usage and identical length and amino acid motifs in the third complementarity-determining regions (CDR3), while a broad repertoire using different combinations of TCR-α/β V and J segments and CDR3 regions was selected by the immunodominant epitope (EBNA4 416-424, designated IVT). Distinct patterns of interaction with the A11–peptide complex were revealed for each AVF- or IVT-specific TCR clonotype by alanine scanning mutagenesis analysis. Blocking of cytotoxic function by antibodies specific for the CD8 coreceptor indicated that, while AVF-specific TCRs are of high affinity, the oligoclonal response to the IVT epitope includes both low- and high-affinity TCRs. Thus, comparison of the memory response to two epitopes derived from the same viral antigen and presented through the same MHC class I allele suggests that immunodominance may correlate with the capacity to maintain a broad TCR repertoire

The Tat Protein of HIV-1 Prevents the Loss of HSV-Specific Memory Adaptive Responses and Favors the Control of Viral Reactivation

The development of therapeutic strategies to control the reactivation of the Herpes Simplex Virus (HSV) is an unaddressed priority. In this study, we evaluated whether Tat, a HIV-1 protein displaying adjuvant functions, could improve previously established HSV-specific memory responses and prevent viral reactivation. To this aim, mice were infected with non-lethal doses of HSV-1 and, 44 days later, injected or not with Tat. Mice were then monitored to check their health status and measure memory HSV-specific cellular and humoral responses. The appearance of symptoms associated with HSV-reactivation was observed at significantly higher frequencies in the control group than in the Tat-treated mice. In addition, the control animals experienced a time-dependent decrease in HSV-specific Immunoglobulin G (IgG), while the Tat-treated mice maintained antibody titers over time. IgG levels were directly correlated with the number of HSV-specific CD8+ T cells, suggesting an effect of Tat on both arms of the adaptive immunity. Consistent with the maintenance of HSV-specific immune memory, Tat-treated mice showed a better control of HSV-1 re-infection. Although further studies are necessary to assess whether similar effects are observed in other models, these results indicate that Tat exerts a therapeutic effect against latent HSV-1 infection and re-infection by favoring the maintenance of adaptive immunity