Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.

Tuberculosis epidemiology in islands: insularity, hosts and trade

Because of their relative simplicity and the barriers to gene flow, islands are ideal systems to study the distribution of biodiversity. However, the knowledge that can be extracted from this peculiar ecosystem regarding epidemiology of economically relevant diseases has not been widely addressed. We used information available in the scientific literature for 10 old world islands or archipelagos and original data on Sicily to gain new insights into the epidemiology of the Mycobacterium tuberculosis complex (MTC). We explored three nonexclusive working hypotheses on the processes modulating bovine tuberculosis (bTB) herd prevalence in cattle and MTC strain diversity: insularity, hosts and trade. Results suggest that bTB herd prevalence was positively correlated with island size, the presence of wild hosts, and the number of imported cattle, but neither with isolation nor with cattle density. MTC strain diversity was positively related with cattle bTB prevalence, presence of wild hosts and the number of imported cattle, but not with island size, isolation, and cattle density. The three most common spoligotype patterns coincided between Sicily and mainland Italy. However in Sicily, these common patterns showed a clearer dominance than on the Italian mainland, and seven of 19 patterns (37%) found in Sicily had not been reported from continental Italy. Strain patterns were not spatially clustered in Sicily. We were able to infer several aspects of MTC epidemiology and control in islands and thus in fragmented host and pathogen populations. Our results point out the relevance of the intensity of the cattle commercial networks in the epidemiology of MTC, and suggest that eradication will prove more difficult with increasing size of the island and its environmental complexity, mainly in terms of the diversity of suitable domestic and wild MTC hosts.

Diversity of LFPs Activated in Different Target Regions by a Common CA3 Input

Identifying the pathways contributing to local field potential (LFP) events and oscillations is essential to determine whether synchronous interregional patterns indicate functional connectivity. Here, we studied experimentally and numerically how different target structures receiving input from a common population shape their LFPs. We focused on the bilateral CA3 that sends gamma-paced excitatory packages to the bilateral CA1, the lateral septum, and itself (recurrent input). The CA3-specific contribution was isolated from multisite LFPs in target regions using spatial discrimination techniques. We found strong modulation of LFPs by target-specific features, including the morphology and population arrangement of cells, the timing of CA3 inputs, volume conduction from nearby targets, and co-activated inhibition. Jointly they greatly affect the LFP amplitude, profile, and frequency characteristics. For instance, ipsilateral (Schaffer) LFPs occluded contralateral ones, and septal LFPs arise mostly from remote sources while local contribution from CA3 input was minor. In the CA3 itself, gamma waves have dual origin from local networks: in-phase excitatory and nearly antiphase inhibitory. Also, waves may have different duration and varying phase in different targets. These results indicate that to explore the cellular basis of LFPs and the functional connectivity between structures, besides identifying the origin population/s, target modifiers should be considered.