The invariants of the Clifford groups

The automorphism group of the Barnes-Wall lattice L_m in dimension 2^m (m not 3) is a subgroup of index 2 in a certain ``Clifford group'' C_m (an extraspecial group of order 2^(1+2m) extended by an orthogonal group). This group and its complex analogue CC_m have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge's 1996 result that the space of invariants for C_m of degree 2k is spanned by the complete weight enumerators of the codes obtained by tensoring binary self-dual codes of length 2k with the field GF(2^m); these are a basis if m >= k-1. We also give new constructions for L_m and C_m: let M be the Z[sqrt(2)]-lattice with Gram matrix [2, sqrt(2); sqrt(2), 2]. Then L_m is the rational part of the mth tensor power of M, and C_m is the automorphism group of this tensor power. Also, if C is a binary self-dual code not generated by vectors of weight 2, then C_m is precisely the automorphism group of the complete weight enumerator of the tensor product of C and GF(2^m). There are analogues of all these results for the complex group CC_m, with ``doubly-even self-dual code'' instead of ``self-dual code''.Comment: Latex, 24 pages. Many small improvement

Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

A nilpotent non abelian group code

The paper reports an example for a nilpotent group code which is not monomially equivalent to some abelian group code

Phospholipid Scramblase 4 (PLSCR4) Regulates Adipocyte Differentiation via PIP3-Mediated AKT Activation

Phospholipid scramblase 4 (PLSCR4) is a member of a conserved enzyme family with high relevance for the remodeling of phospholipid distribution in the plasma membrane and the regulation of cellular signaling. While PLSCR1 and -3 are involved in the regulation of adipose-tissue expansion, the role of PLSCR4 is so far unknown. PLSCR4 is significantly downregulated in an adipose-progenitor-cell model of deficiency for phosphatase and tensin homolog (PTEN). PTEN acts as a tumor suppressor and antagonist of the growth and survival signaling phosphoinositide 3-kinase (PI3K)/AKT cascade by dephosphorylating phosphatidylinositol-3,4,5-trisphosphate (PIP3). Patients with PTEN germline deletion frequently develop lipomas. The underlying mechanism for this aberrant adipose-tissue growth is incompletely understood. PLSCR4 is most highly expressed in human adipose tissue, compared with other phospholipid scramblases, suggesting a specific role of PLSCR4 in adipose-tissue biology. In cell and mouse models of lipid accumulation, we found PLSCR4 to be downregulated. We observed increased adipogenesis in PLSCR4-knockdown adipose progenitor cells, while PLSCR4 overexpression attenuated lipid accumulation. PLSCR4 knockdown was associated with increased PIP3 levels and the activation of AKT. Our results indicated that PLSCR4 is a regulator of PI3K/AKT signaling and adipogenesis and may play a role in PTEN-associated adipose-tissue overgrowth and lipoma formation

Almudena Armenta. Artistas que pudieron ser

Las obras que contemplamos han llegado a cobrar realidad gracias a mujeres solidarias y enlazadas entre sí por familia. En aquella sociedad de la que procede la artista, las mujeres compartían mensajes y se transmitían entre sí aquello que iban fraguado en su espíritu para que, la que lograse acceder a algún distinguido ámbito social, en esta ocasión fue artístico, pudiese dar cuenta de ese universo propio que se las obligaba a ocultar en sus trayectorias vitales. Almudena Armenta es una de las elegidas. Su esfuerzo, creatividad y el apoyo por parte de las mujeres de su familia, además de su resolución y a pesar de toda resistencia social y familiar, la han convertido en portavoz de una saga que vivió en aquella época compleja. Ella se jugó su destino en un momento en el que se cerraba una puerta y se abría definitivamente otra, que daría paso a mundos en donde las mujeres ya podrían expresarse por sí mismas en todos los ámbitos. Sin embargo, las formas de vida y de creatividad de muchas de ellas se quedaron ahogadas en la determinación de un mundo que hoy percibimos como obsoleto e injusto. Sus referentes están todavía en los años sesenta y setenta, y ella los convierte en obras de arte de las que emanan una enorme sensibilidad y belleza. Su material de base, en realidad, son propiedades femeninas, secretos callados reducidos a símbolos materiales impregnados de emoción que ahora adquieren un trascendental valor testimonial

From Skew-Cyclic Codes to Asymmetric Quantum Codes

We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties. If $C$ is a linear $[n,k,d]_4$-code, then $S(C)$ is an additive $(2n,2^{2k},2d)_4$-code. If $C$ is an additive cyclic code then $S(C)$ is an additive quasi-cyclic code of index $2$. Moreover, if $C$ is a module $\theta$-cyclic code, a recently introduced type of code which will be explained below, then $S(C)$ is equivalent to an additive cyclic code if $n$ is odd and to an additive quasi-cyclic code of index $2$ if $n$ is even. Given any $(n,M,d)_4$-code $C$, the code $S(C)$ is self-orthogonal under the trace Hermitian inner product. Since the mapping $S$ preserves nestedness, it can be used as a tool in constructing additive asymmetric quantum codes.Comment: 16 pages, 3 tables, submitted to Advances in Mathematics of Communication

Small integral membrane protein 10 like 1 downregulation enhances differentiation of adipose progenitor cells

Small integral membrane protein 10 like 1 (SMIM10L1) was identified by RNA sequencing as the most significantly downregulated gene in Phosphatase and Tensin Homologue (PTEN) knockdown adipose progenitor cells (APCs). PTEN is a tumor suppressor that antagonizes the growth promoting Phosphoinositide 3-kinase (PI3K)/AKT/mechanistic Target of Rapamycin (mTOR) cascade. Diseases caused by germline pathogenic variants in PTEN are summarized as PTEN Hamartoma Tumor Syndrome (PHTS). This overgrowth syndrome is associated with lipoma formation, especially in pediatric patients. The mechanisms underlying this adipose tissue dysfunction remain elusive. We observed that SMIM10L1 downregulation in APCs led to an enhanced adipocyte differentiation in two- and three-dimensional cell culture and increased expression of adipogenesis markers. Furthermore, SMIM10L1 knockdown cells showed a decreased expression of PTEN, pointing to a mutual crosstalk between PTEN and SMIM10L1. In line with these observations, SMIM10L1 knockdown cells showed increased activation of PI3K/AKT/mTOR signaling and concomitantly increased expression of the adipogenic transcription factor SREBP1. We computationally predicted an α-helical structure and membrane association of SMIM10L1. These results support a specific role for SMIM10L1 in regulating adipogenesis, potentially by increasing PI3K/AKT/mTOR signaling, which might be conducive to lipoma formation in pediatric patients with PHTS

Magic state distillation in all prime dimensions using quantum Reed-Muller codes

We propose families of protocols for magic state distillation -- important components of fault tolerance schemes --- for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic state distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarising noise (36.3%) and the efficiency measure know as "yield", where, for a large region of parameters, it outperforms its qubit counterpart by many orders of magnitude.Comment: Updated from V1 to include results on the remarkable d=5 cas

Model-Based and Model-Free Control Predicts Alcohol Consumption Developmental Trajectory in Young Adults: A 3-Year Prospective Study.

BACKGROUND: A shift from goal-directed toward habitual control has been associated with alcohol dependence. Whether such a shift predisposes to risky drinking is not yet clear. We investigated how goal-directed and habitual control at age 18 predict alcohol use trajectories over the course of 3 years. METHODS: Goal-directed and habitual control, as informed by model-based (MB) and model-free (MF) learning, were assessed with a two-step sequential decision-making task during functional magnetic resonance imaging in 146 healthy 18-year-old men. Three-year alcohol use developmental trajectories were based on either a consumption score from the self-reported Alcohol Use Disorders Identification Test (assessed every 6 months) or an interview-based binge drinking score (grams of alcohol/occasion; assessed every year). We applied a latent growth curve model to examine how MB and MF control predicted the drinking trajectory. RESULTS: Drinking behavior was best characterized by a linear trajectory. MB behavioral control was negatively associated with the development of the binge drinking score; MF reward prediction error blood oxygen level-dependent signals in the ventromedial prefrontal cortex and the ventral striatum predicted a higher starting point and steeper increase of the Alcohol Use Disorders Identification Test consumption score over time, respectively. CONCLUSIONS: We found that MB behavioral control was associated with the binge drinking trajectory, while the MF reward prediction error signal was closely linked to the consumption score development. These findings support the idea that unbalanced MB and MF control might be an important individual vulnerability in predisposing to risky drinking behavior