On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode

AbstractIn the Candecomp/Parafac (CP) model, a three-way array X̲ is written as the sum of R outer vector product arrays and a residual array. The former comprise the columns of the component matrices A, B and C. For fixed residuals, (A,B,C) is unique up to trivial ambiguities, if 2R+2 is less than or equal to the sum of the k-ranks of A, B and C. This classical result was shown by Kruskal in 1977. In this paper, we consider the case where one of A, B, C has full column rank, and show that in this case Kruskal’s uniqueness condition implies a recently obtained uniqueness condition. Moreover, we obtain Kruskal-type uniqueness conditions that are weaker than Kruskal’s condition itself. Also, for (A,B,C) with rank(A)=R-1 and C full column rank, we obtain easy-to-check necessary and sufficient uniqueness conditions. We extend our results to the Indscal decomposition in which the array X̲ has symmetric slices and A=B is imposed. We consider the real-valued CP and Indscal decompositions, but our results are also valid for their complex-valued counterparts

Rate of inter-herd transmission of classical swine fever virus by different types of contact during the 1997-8 epidemic in The Netherlands

In this study we quanti®ed the rate at which classical swine fever had been transmitted by several different types of inter-herd contact during the 1997±8 epidemic in The Netherlands. During that epidemic 428 CSFV-infected pig herds were detected, 403 of which were include in this study. The estimated rates of transmission were 0±065 per shipment of live pigs, 0±011 per contact by a pig transportation lorry, 0±0068 per person contact, 0±0007 per dose of semen, 0±0065 per contact with a potentially contaminated pig assembly point, 0±027 per week per infected herd within a radius of 500 metres and 0±0078 per week per infected herd at a distance between 500 and 1000 metres. These transmission rates can be used to optimize the strategy to stop future epidemics of CSF in The Netherlands. In addition, the analysis demonstrated in this paper, can be used to quantify CSFV transmission rates from other epidemics

Symmetry transformations for square sliced three-way arrays, with applications to their typical rank

AbstractThe typical 3-tensorial rank has been much studied over algebraically closed fields, but very little has been achieved in the way of results pertaining to the real field. The present paper examines the typical 3-tensorial rank over the real field, when the slices of the array involved are square matrices. The typical rank of 3×3×3 arrays is shown to be five. The typical rank of p×q×q arrays is shown to be larger than q+1 unless there are only two slices (p=2), or there are three slices of order 2×2 (p=3 and q=2). The key result is that when the rank is q+1, there usually exists a rank-preserving transformation of the array to one with symmetric slices

The elevation of the anion gap in steady state chronic kidney disease may be less prominent than generally accepted

BACKGROUND: A presumed cause of metabolic acidosis in chronic kidney disease (CKD) is accumulation of unmeasured anions, leading to a high anion gap (AG). In patients with CKD with a high AG, only minor increases are expected. The aim of this study is to evaluate the magnitude of the AG in documented steady state CKD to examine the effect of CKD on a high-AG metabolic acidosis (HAGMA).METHODS: In this cross-sectional study the AG, bicarbonate, and chloride were evaluated in 1045 blood and urine samples of 501 patients with steady state CKD in the outpatient clinic. The influence of phosphate, albumin and potassium on the AG were evaluated.RESULTS: The mean AG increased from 8.8 mEq/l (±1.57) in CKD stage 1 to 11.2 mEq/l (±2.22) in CKD stage 5 ( P &lt; 0.001). Correction for albumin or phosphate did not influence the magnitude of the AG. Correction for potassium did alter the prevalence of HAGMA, but not the severity. [HCO 3 -] decreased between CKD stages 1 and 5 by 5.1 mEq/l. The [Cl -] increased by 2.6 mEq/l between CKD stages 1 and 5. CONCLUSIONS: The elevation of the AG in patients with steady state CKD is limited and less pronounced than the decrease in [HCO 3 -]. Normal AG metabolic acidosis seems to be more important in CKD than HAGMA. The CKD stage and the magnitude of the AG should be taken into account when evaluating a patient with HAGMA. This study suggests that an AG &gt;15 mEq/l is rarely due to renal failure alone. </p

Oxalate nephropathy in an elderly patient with newly diagnosed celiac disease:a case report

Oxalate nephropathy, due to secondary hyperoxaluria has widely been described in gastrointestinal diseases. However, reports of oxalate nephropathy in newly diagnosed celiac disease are rare. A 72-year-old Caucasian male presented to the hospital with abdominal discomfort and acute renal insufficiency with a creatinine of 290 µmol/L. The clinical course, laboratory results and urinalysis were suspect for tubular injury. Renal biopsy showed calcium oxalate depositions. Elevated plasma and urine oxalate levels established the diagnosis oxalate nephropathy. The abdominal complaints with steatorrhea and positive anti-tissue transglutaminase antibodies were diagnosed as celiac disease, which was confirmed after duodenal biopsies. Treatment with prednisone, and gluten-free, low oxalate and normal calcium diet, lowered the plasma oxalate levels and improved his renal function. Decreased absorption of free fatty acids can lead to increased free oxalate in the colon due to the binding of free fatty acids to calcium, preventing the formation of the less absorbable calcium oxalate in the colon. Oxalate dispositions in the kidney can lead to acute tubular injury and chronic renal insufficiency. Celiac disease is therefore one of the intestinal diseases that can lead to hyperoxaluria and oxalate nephropathy.</p

Self-written waveguides in photopolymerizable resins

We study the optically-induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and relative power of the input beams, and suggest an improved analytical model that describes the growth of single self-written waveguides and the main features of their interaction in photosensitive materials.Comment: 3 pages, 3 figure

New nonlinear dielectric materials: Linear electrorheological fluids under the influence of electrostriction

The usual approach to the development of new nonlinear dielectric materials focuses on the search for materials in which the components possess an inherently large nonlinear dielectric response. In contrast, based on thermodynamics, we have presented a first-principles approach to obtain the electrostriction-induced effective third-order nonlinear susceptibility for the electrorheological (ER) fluids in which the components have inherent linear, rather than nonlinear, responses. In detail, this kind of nonlinear susceptibility is in general of about the same order of magnitude as the compressibility of the linear ER fluid at constant pressure. Moreover, our approach has been demonstrated in excellent agreement with a different statistical method. Thus, such linear ER fluids can serve as a new nonlinear dielectric material.Comment: 11 page