Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Applicability of an assessment model for healthcare information systems in a public hospital

Assessment processes are essential to guarantee quality and continuous improvement of software in healthcare, as they measure software attributes in their lifecycle, verify the degree of alignment between the software and its objectives and identify unpredicted events. This article analyses the use of an assessment model based on software metrics for three healthcare information systems from a public hospital that provides secondary and tertiary care in the region of Ribeirão Preto. Compliance with the metrics was investigated using questionnaires in guided interviews of the system analysts responsible for the applications. The outcomes indicate that most of the procedures specified in the model can be adopted to assess the systems that serves the organization, particularly in the attributes of compatibility, reliability, safety, portability and usability.

Efficient and precise interactive hand tracking through joint, continuous optimization of pose and correspondences

Fully articulated hand tracking promises to enable fundamentally new interactions with virtual and augmented worlds, but the limited accuracy and efficiency of current systems has prevented widespread adoption. Today's dominant paradigm uses machine learning for initialization and recovery followed by iterative model-fitting optimization to achieve a detailed pose fit. We follow this paradigm, but make several changes to the model-fitting, namely using: (1) a more discriminative objective function; (2) a smooth-surface model that provides gradients for non-linear optimization; and (3) joint optimization over both the model pose and the correspondences between observed data points and the model surface. While each of these changes may actually increase the cost per fitting iteration, we find a compensating decrease in the number of iterations. Further, the wide basin of convergence means that fewer starting points are needed for successful model fitting. Our system runs in real-time on CPU only, which frees up the commonly over-burdened GPU for experience designers. The hand tracker is efficient enough to run on low-power devices such as tablets. We can track up to several meters from the camera to provide a large working volume for interaction, even using the noisy data from current-generation depth cameras. Quantitative assessments on standard datasets show that the new approach exceeds the state of the art in accuracy. Qualitative results take the form of live recordings of a range of interactive experiences enabled by this new approach.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Personalization of Electronic Nicotine Delivery Systems Toxicological impact in in-vivo model

Electronic nicotine delivery systems (ENDS) use has recently grown. E-cig generates carcinogenic chemical compounds and reactive oxygen species (ROS). Carbonyls and ROS are formed when the liquid comes into contact with the heating element. In this study the chemical and biological effects of coil resistance applied on the same device were investigated. A preliminary in-vivo study the new heat-not-burn devices (IQOS®) has been conducted to evaluate the effect of the device on antioxidant biomarkers. The amount of formaldehyde, acetaldehyde, acrolein was measured by GC-MS analysis. The two e-liquids used for carbonyls detection differed only for the presence of nicotine. The nicotine-free liquid was then used for the detection of ROS in the aerosol. The impact of the non-nicotine vapor on cell viability in H1299 human lung carcinoma cells, as well as the biological effects in a rat model of e-cig aerosol exposure, were also evaluated. After the exposure of Sprague Dawley rats to e-cig and IQOS® aerosol, the effect of 28-day treatment was examined on enzymatic and non-enzymatic antioxidant response, lung inflammation, blood homeostasis and tissue damage by using scanning electron microscope (SEM) technique. The results show a significant correlation between the low resistance and the generation of higher concentrations of the selected carbonyls and ROS in aerosols. Cell viability was reduced with an inverse relation to coil resistance. The experimental model highlighted an impairment of the pulmonary antioxidant and detoxifying machinery. Frames from SEM show disorganization of alveolar and bronchial epithelium. IQOS® exposed animals shows a significant production of ROS related to the unbalance of antioxidant defense and alteration of macromolecule integrity. This research demonstrates how several toxicological aspects can potentially occur in e-cig consumers who use low resistance device coupled with nicotine-free liquid. ENDS may expose users to hazardous compounds, which, may promote chronic pathologies and degenerative diseases.

High-resolution stratigraphy and seismic site characterization of late Quaternary paleovalley systems (Adriatic coastal plain, Italy)

In highly urbanized coastal lowlands, effective site characterization is crucial for assessing seismic risk. It requires a comprehensive stratigraphic analysis of the shallow subsurface, coupled with the precise assessment of the geophysical properties of buried deposits. In this context, late Quaternary paleovalley systems, shallowly buried fluvial incisions formed during the Late Pleistocene sea-level fall and filled during the Holocene sea-level rise, are crucial for understanding seismic amplification due to their soft sediment infill and sharp lithologic contrasts. In this research, we conducted high-resolution stratigraphic analyses of two regions, the Pescara and Manfredonia areas along the Adriatic coastline of Italy, to delineate the geometries and facies architecture of two paleovalley systems. Furthermore, we carried out geophysical investigations to characterize the study areas and perform seismic response analyses. We tested the microtremor-based horizontal-to-vertical spectral ratio as a mapping tool to reconstruct the buried paleovalley geometries. We evaluated the relationship between geological and geophysical data and identified the stratigraphic surfaces responsible for the observed resonances. To perform seismic response analysis of the Pescara paleovalley system, we integrated the stratigraphic framework with microtremor and shear wave velocity measurements. The seismic response analysis highlights strong seismic amplifications in frequency ranges that can interact with a wide variety of building types. Additionally, we explored the applicability of artificial intelligence in performing facies analysis from borehole images. We used a robust dataset of high-resolution digital images from continuous sediment cores of Holocene age to outline a novel, deep-learning-based approach for performing automatic semantic segmentation directly on core images, leveraging the power of convolutional neural networks. We propose an automated model to rapidly characterize sediment cores, reproducing the sedimentologist's interpretation, and providing guidance for stratigraphic correlation and subsurface reconstructions.

A Microleakage Study Of Gutta-percha/ah Plus And Resilon/real Self-etch Systems After Different Irrigation Protocols.

The development and maintenance of the sealing of the root canal system is the key to the success of root canal treatment. The resin-based adhesive material has the potential to reduce the microleakage of the root canal because of its adhesive properties and penetration into dentinal walls. Moreover, the irrigation protocols may have an influence on the adhesiveness of resin-based sealers to root dentin. The objective of the present study was to evaluate the effect of different irrigant protocols on coronal bacterial microleakage of gutta-percha/AH Plus and Resilon/Real Seal Self-etch systems. One hundred ninety pre-molars were used. The teeth were divided into 18 experimental groups according to the irrigation protocols and filling materials used. The protocols used were: distilled water; sodium hypochlorite (NaOCl)+eDTA; NaOCl+H3PO4; NaOCl+eDTA+chlorhexidine (CHX); NaOCl+H3PO4+CHX; CHX+eDTA; CHX+ H3PO4; CHX+eDTA+CHX and CHX+H3PO4+CHX. Gutta-percha/AH Plus or Resilon/Real Seal Se were used as root-filling materials. The coronal microleakage was evaluated for 90 days against Enterococcus faecalis. Data were statistically analyzed using Kaplan-Meier survival test, Kruskal-Wallis and Mann-Whitney tests. No significant difference was verified in the groups using chlorhexidine or sodium hypochlorite during the chemo-mechanical preparation followed by eDTA or phosphoric acid for smear layer removal. The same results were found for filling materials. However, the statistical analyses revealed that a final flush with 2% chlorhexidine reduced significantly the coronal microleakage. A final flush with 2% chlorhexidine after smear layer removal reduces coronal microleakage of teeth filled with gutta-percha/AH Plus or Resilon/Real Seal SE.

Does The Reciproc File Remove Root Canal Bacteria And Endotoxins As Effectively As Multifile Rotary Systems?

To evaluate the effectiveness of Reciproc for the removal of cultivable bacteria and endotoxins from root canals in comparison with multifile rotary systems. The root canals of forty human single-rooted mandibular pre-molars were contaminated with an Escherichia coli suspension for 21 days and randomly assigned to four groups according to the instrumentation system: GI - Reciproc (VDW); GII - Mtwo (VDW); GIII - ProTaper Universal (Dentsply Maillefer); and GIV -FKG Race(™) (FKG Dentaire) (n = 10 per group). Bacterial and endotoxin samples were taken with a sterile/apyrogenic paper point before (s1) and after instrumentation (s2). Culture techniques determined the colony-forming units (CFU) and the Limulus Amebocyte Lysate assay was used for endotoxin quantification. Results were submitted to paired t-test and anova. At s1, bacteria and endotoxins were recovered in 100% of the root canals investigated (40/40). After instrumentation, all systems were associated with a highly significant reduction of the bacterial load and endotoxin levels, respectively: GI - Reciproc (99.34% and 91.69%); GII - Mtwo (99.86% and 83.11%); GIII - ProTaper (99.93% and 78.56%) and GIV - FKG Race(™) (99.99% and 82.52%) (P < 0.001). No statistical difference were found amongst the instrumentation systems regarding bacteria and endotoxin removal (P > 0.01). The reciprocating single file, Reciproc, was as effective as the multifile rotary systems for the removal of bacteria and endotoxins from root canals.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Dentine Bond Strength And Antimicrobial Activity Evaluation Of Adhesive Systems.

This study evaluated the dentine bond strength (BS) and the antibacterial activity (AA) of six adhesives against strict anaerobic and facultative bacteria. Three adhesives containing antibacterial components (Gluma 2Bond (glutaraldehyde)/G2B, Clearfil SE Protect (MDPB)/CSP and Peak Universal Bond (PUB)/chlorhexidine) and the same adhesive versions without antibacterial agents (Gluma Comfort Bond/GCB, Clearfil SE Bond/CSB and Peak LC Bond/PLB) were tested. The AA of adhesives and control groups was evaluated by direct contact method against four strict anaerobic and four facultative bacteria. After incubation, according to the appropriate periods of time for each microorganism, the time to kill microorganisms was measured. For BS, the adhesives were applied according to manufacturers' recommendations and teeth restored with composite. Teeth (n=10) were sectioned to obtain bonded beams specimens, which were tested after artificial saliva storage for one week and one year. BS data were analyzed using two-way ANOVA and Tukey test. Saliva storage for one year reduces the BS only for GCB. In general G2B and GCB required at least 24h for killing microorganisms. PUB and PLB killed only strict anaerobic microorganisms after 24h. For CSP the average time to eliminate the Streptococcus mutans and strict anaerobic oral pathogens was 30min. CSB showed no AA against facultative bacteria, but had AA against some strict anaerobic microorganisms. Storage time had no effect on the BS for most of the adhesives. The time required to kill bacteria depended on the type of adhesive and never was less than 10min. Most of the adhesives showed stable bond strength after one year and the Clearfil SE Protect may be a good alternative in restorative procedures performed on dentine, considering its adequate bond strength and better antibacterial activity.

Self-etch Adhesive Systems: A Literature Review.

This paper presents the state of the art of self-etch adhesive systems. Four topics are shown in this review and included: the historic of this category of bonding agents, bonding mechanism, characteristics/properties and the formation of acid-base resistant zone at enamel/dentin-adhesive interfaces. Also, advantages regarding etch-and-rinse systems and classifications of self-etch adhesive systems according to the number of steps and acidity are addressed. Finally, issues like the potential durability and clinical importance are discussed. Self-etch adhesive systems are promising materials because they are easy to use, bond chemically to tooth structure and maintain the dentin hydroxyapatite, which is important for the durability of the bonding.

Chronic Continuous Exenatide Infusion Does Not Cause Pancreatic Inflammation And Ductal Hyperplasia In Non-human Primates.

In this study, we aimed to evaluate the effects of exenatide (EXE) treatment on exocrine pancreas of nonhuman primates. To this end, 52 baboons (Papio hamadryas) underwent partial pancreatectomy, followed by continuous infusion of EXE or saline (SAL) for 14 weeks. Histological analysis, immunohistochemistry, Computer Assisted Stereology Toolbox morphometry, and immunofluorescence staining were performed at baseline and after treatment. The EXE treatment did not induce pancreatitis, parenchymal or periductal inflammatory cell accumulation, ductal hyperplasia, or dysplastic lesions/pancreatic intraepithelial neoplasia. At study end, Ki-67-positive (proliferating) acinar cell number did not change, compared with baseline, in either group. Ki-67-positive ductal cells increased after EXE treatment (P = 0.04). However, the change in Ki-67-positive ductal cell number did not differ significantly between the EXE and SAL groups (P = 0.13). M-30-positive (apoptotic) acinar and ductal cell number did not change after SAL or EXE treatment. No changes in ductal density and volume were observed after EXE or SAL. Interestingly, by triple-immunofluorescence staining, we detected c-kit (a marker of cell transdifferentiation) positive ductal cells co-expressing insulin in ducts only in the EXE group at study end, suggesting that EXE may promote the differentiation of ductal cells toward a β-cell phenotype. In conclusion, 14 weeks of EXE treatment did not exert any negative effect on exocrine pancreas, by inducing either pancreatic inflammation or hyperplasia/dysplasia in nonhuman primates.

Influence of different adhesive systems on the pull-out bond strength of glass fiber posts

This in vitro study evaluated the tensile bond strength of glass fiber posts (Reforpost - Angelus-Brazil) cemented to root dentin with a resin cement (RelyX ARC - 3M/ESPE) associated with two different adhesive systems (Adper Single Bond - 3M/ESPE and Adper Scotchbond Multi Purpose (MP) Plus - 3M/ESPE), using the pull-out test. Twenty single-rooted human teeth with standardized root canals were randomly assigned to 2 groups (n=10): G1- etching with 37% phosphoric acid gel (3M/ESPE) + Adper Single Bond + #1 post (Reforpost - Angelus) + four #1 accessory posts (Reforpin - Angelus) + resin cement; G2- etching with 37% phosphoric acid gel + Adper Scotchbond MP Plus + #1 post + four #1 accessory posts + resin cement. The specimens were stored in distilled water at 37°C for 7 days and submitted to the pull-out test in a universal testing machine (EMIC) at a crosshead speed of 0.5 mm/min. The mean values of bond strength (kgf) and standard deviation were: G1- 29.163 ± 7.123; G2- 37.752 ±13.054. Statistical analysis (Student's t-test; a=0.05 showed no statistically significant difference (p<0.05) between the groups. Adhesive bonding failures between resin cement and root canal dentin surface were observed in both groups, with non-polymerized resin cement in the apical portion of the post space when Single Bond was used (G1). The type of adhesive system employed on the fiber post cementation did not influence the pull-out bond strength.

Shear bond strength of self-etch and total-etch bonding systems at different dentin depths

The purpose of this study was to evaluate the dentin shear bond strength of four adhesive systems (Adper Single Bond 2, Adper Prompt L-Pop, Magic Bond DE and Self Etch Bond) in regards to buccal and lingual surfaces and dentin depth. Forty extracted third molars had roots removed and crowns bisected in the mesiodistal direction. The buccal and lingual surfaces were fixed in a PVC/acrylic resin ring and were divided into buccal and lingual groups assigned to each selected adhesive. The same specimens prepared for the evaluation of superficial dentin shear resistance were used to evaluate the different depths of dentin. The specimens were identified and abraded at depths of 0.5, 1.0, 1.5 and 2.0 mm. Each depth was evaluated by ISO TR 11405 using an EMIC-2000 machine regulated at 0.5 mm/min with a 200 Kgf load cell. We performed statistical analyses on the results (ANOVA, Tukey and Scheffé tests). Data revealed statistical differences (p < 0.01) in the adhesive and depth variation as well as adhesive/depth interactions. The Adper Single Bond 2 demonstrated the highest mean values of shear bond strength. The Prompt L-Pop product, a self-etching adhesive, revealed higher mean values compared with Magic Bond DE and Self Etch Bond adhesives, a total and self-etching adhesive respectively. It may be concluded that the shear bond strength of dentin is dependent on material (adhesive system), substrate depth and adhesive/depth interaction.