The Zak transform: a framework for quantum computation with the Gottesman-Kitaev-Preskill code

The Gottesman-Kitaev-Preskill (GKP) code encodes a qubit into a bosonic mode using periodic wavefunctions. This periodicity makes the GKP code a natural setting for the Zak transform, which is tailor-made to provide a simple description for periodic functions. We review the Zak transform and its connection to a Zak basis of states in Hilbert space, decompose the shift operators that underpin the stabilizers and the correctable errors, and we find that Zak transforms of the position wavefunction appear naturally in GKP error correction. We construct a new bosonic subsystem decomposition (SSD) -- the modular variable SSD -- by dividing a mode's Hilbert space, expressed in the Zak basis, into that of a virtual qubit and a virtual gauge mode. Tracing over the gauge mode gives a logical-qubit state, and preceding the trace with a particular logical-gauge interaction gives a different logical state -- that associated to GKP error correction.Comment: 15 pages, 5 figure

Developmental profiles of young children with autism spectrum disorder and global developmental delay: A study with the Griffiths III scales

The purpose of this study was to identify developmental profiles associated with autism spectrum disorder (ASD) and global developmental delay (DD) in pre-school aged Italian children. Developmental profiles were evaluated by means of a standardized tool widely used for the assessment of psychomotor development in early childhood, the Griffiths III scales, recently adapted and standardized for the Italian population. Specifically, we compared the Griffiths III profiles of children with ASD and DD (ASD + DD) with those of children with DD alone. Moreover, we inspected the psychometric function of single items by comparing children with ASD + DD and children with DD with typically developing (TD) children from the Griffiths III normative sample. In this way, we aimed to isolate the effects of each diagnostic class on psychomotor abilities and on the psychometric function of single items. The ASD + DD and DD groups were found to share the presence of lower age equivalent scores relative to their chronological age in all the developmental domains considered: Foundations of Learning, Language and Communication, Eye and Hand Coordination, Personal–Social-Emotional and Gross Motor Skills. However, the DD group displayed a homogeneous profile with similar levels of delay in all developmental domains, while children with ASD + DD exhibited relative weaknesses in the Language and Communication and Personal–Social-Emotional scales. The analysis of the psychometric function drawn for each item has confirmed different profiles in social-communicative and non-verbal items between the two diagnostic groups and in relation to TD normative sample. The Griffiths III is a valid psychometric tool for identifying atypical developmental profiles and its use may be recommended during the diagnostic process of ASD and DD, to detect specific strengths and weaknesses and guide person-centered treatment

Argas (Persicargas) persicus (Oken, 1818) (Ixodida: Argasidae) in Sicily with considerations about its Italian and West-Mediterranean distribution.

Recently, in the province of Trapani (Western Sicily), some overwintering specimens of the argasid tick Argas (Persicargas) persicus (Oken, 1818) were observed and collected. Morphological and genetic analysis were utilized in order to reach a definitive identification. The species was found in two semi-natural sites where, having been found repeatedly, its presence does not appear accidental. Moreover the characteristics of the Sicilian findings seem to exclude a human-induced spread. This record, the first regarding Sicily and South Italy, is discussed together with the previous doubtful citations for Italy. These findings revalue not only all the old citations for Italy but also the hypothesis that the Mediterranean distribution of this argasid is of a natural origin

Postural Control in Children with Cerebellar Ataxia

Controlling posture, i.e., governing the ensemble of involuntary muscular activities that manage body equilibrium, represents a demanding function in which the cerebellum plays a key role. Postural activities are particularly important during gait initiation when passing from quiet standing to locomotion. Indeed, several studies used such motor task for evaluating pathological conditions, including cerebellar disorders. The linkage between cerebellum maturation and the development of postural control has received less attention. Therefore, we evaluated postural control during quiet standing and gait initiation in children affected by a slow progressive generalized cerebellar atrophy (SlowP) or non-progressive vermian hypoplasia (Joubert syndrome, NonP), compared to that of healthy children (H). Despite the similar clinical evaluation of motor impairments in NonP and SlowP, only SlowP showed a less stable quiet standing and a shorter and slower first step than H. Moreover, a descriptive analysis of lower limb and back muscle activities suggested a more severe timing disruption in SlowP. Such differences might stem from the extent of cerebellar damage. However, literature reports that during childhood, neural plasticity of intact brain areas could compensate for cerebellar agenesis. We thus proposed that the difference might stem from disease progression, which contrasts the consolidation of compensatory strategies

Structural and connectivity parameters reveal spared connectivity in young patients with non-progressive compared to slow-progressive cerebellar ataxia

INTRODUCTION: Within Pediatric Cerebellar Ataxias (PCAs), patients with non-progressive ataxia (NonP) surprisingly show postural motor behavior comparable to that of healthy controls, differently to slow-progressive ataxia patients (SlowP). This difference may depend on the building of compensatory strategies of the intact areas in NonP brain network. METHODS: Eleven PCAs patients were recruited: five with NonP and six with SlowP. We assessed volumetric and axonal bundles alterations with a multimodal approach to investigate whether eventual spared connectivity between basal ganglia and cerebellum explains the different postural motor behavior of NonP and SlowP patients. RESULTS: Cerebellar lobules were smaller in SlowP patients. NonP patients showed a lower number of streamlines in the cerebello-thalamo-cortical tracts but a generalized higher integrity of white matter tracts connecting the cortex and the basal ganglia with the cerebellum. DISCUSSION: This work reveals that the axonal bundles connecting the cerebellum with basal ganglia and cortex demonstrate a higher integrity in NonP patients. This evidence highlights the importance of the cerebellum-basal ganglia connectivity to explain the different postural motor behavior of NonP and SlowP patients and support the possible compensatory role of basal ganglia in patients with stable cerebellar malformation

Concurrent AFG3L2 and SPG7 mutations associated with syndromic parkinsonism and optic atrophy with aberrant OPA1 processing and mitochondrial network fragmentation

Mitochondrial dynamics and quality control are crucial for neuronal survival and their perturbation is a major cause of neurodegeneration. m-AAA complex is an ATP-dependent metalloprotease located in the inner mitochondrial membrane and involved in protein quality control. Mutations in the m-AAA subunits AFG3L2 and paraplegin are associated with autosomal dominant spinocerebellar ataxia (SCA28) and autosomal recessive hereditary spastic paraplegia (SPG7), respectively. We report a novel m-AAA-associated phenotype characterized by early-onset optic atrophy with spastic ataxia and L-Dopa-responsive parkinsonism. The proband carried a de-novo AFG3L2 heterozygous mutation (p.R468C) along with a heterozygous maternally-inherited intragenic deletion of SPG7. Functional analysis in yeast demonstrated the pathogenic role of AFG3L2 p.R468C mutation shedding light on its pathogenic mechanism. Analysis of patient's fibroblasts showed an abnormal processing pattern of OPA1, a dynamin-related protein essential for mitochondrial fusion and responsible for most cases of hereditary optic atrophy. Consistently, assessment of mitochondrial morphology revealed a severe fragmentation of the mitochondrial network, not observed in SCA28 and SPG7 patients\u2019 cells. This case suggests that coincidental mutations in both components of the mitochondrial m-AAA protease may result in a complex phenotype and reveals a crucial role for OPA1 processing in the pathogenesis of neurodegenerative disease caused by m-AAA defects