Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Intact imitation of emotional facial actions in autism spectrum conditions.

It has been proposed that there is a core impairment in autism spectrum conditions (ASC) to the mirror neuron system (MNS): If observed actions cannot be mapped onto the motor commands required for performance, higher order sociocognitive functions that involve understanding another person's perspective, such as theory of mind, may be impaired. However, evidence of MNS impairment in ASC is mixed. The present study used an 'automatic imitation' paradigm to assess MNS functioning in adults with ASC and matched controls, when observing emotional facial actions. Participants performed a pre-specified angry or surprised facial action in response to observed angry or surprised facial actions, and the speed of their action was measured with motion tracking equipment. Both the ASC and control groups demonstrated automatic imitation of the facial actions, such that responding was faster when they acted with the same emotional expression that they had observed. There was no difference between the two groups in the magnitude of the effect. These findings suggest that previous apparent demonstrations of impairments to the MNS in ASC may be driven by a lack of visual attention to the stimuli or motor sequencing impairments, and therefore that there is, in fact, no MNS impairment in ASC. We discuss these findings with reference to the literature on MNS functioning and imitation in ASC, as well as theories of the role of the MNS in sociocognitive functioning in typical development.

Comparison of algal and fish sources on the oxidative stability of poultry meat and its enrichment with omega-3 polyunsaturated fatty acids

Human consumption of long-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) is below recommendations, and enriching chicken meat (by incorporating LC n-3 PUFA into broiler diets) is a viable means of increasing consumption. Fish oil is the most common LC n-3 PUFA supplement used but is unsustainable and reduces the oxidative stability of the meat. The objective of this experiment was to compare fresh fish oil (FFO) with fish oil encapsulated (EFO) in a gelatin matrix (to maintain its oxidative stability) and algal biomass at a low (LAG, 11), medium (MAG, 22), or high (HAG, 33 g/kg of diet) level of inclusion. The C22:6n-3 contents of the FFO, EFO, and MAG diets were equal. A control (CON) diet using blended vegetable oil was also made. As-hatched 1-d-old Ross 308 broilers (144) were reared (21 d) on a common starter diet then allocated to treatment pens (4 pens per treatment, 6 birds per pen) and fed treatment diets for 21 d before being slaughtered. Breast and leg meat was analyzed (per pen) for fatty acids, and cooked samples (2 pens per treatment) were analyzed for volatile aldehydes. Concentrations (mg/100 g of meat) of C20:5n-3, C22:5n-3, and C22:6n-3 were (respectively) CON: 4, 15, 24; FFO: 31, 46, 129; EFO: 18, 27, 122; LAG: 9, 19, 111; MAG: 6, 16, 147; and HAG: 9, 14, 187 (SEM: 2.4, 3.6, 13.1) in breast meat and CON: 4, 12, 9; FFO: 58, 56, 132; EFO: 63, 49, 153; LAG: 13, 14, 101; MAG: 11, 15, 102; HAG: 37, 37, 203 (SEM: 7.8, 6.7, 14.4) in leg meat. Cooked EFO and HAG leg meat was more oxidized (5.2 mg of hexanal/kg of meat) than the other meats (mean 2.2 mg/kg, SEM 0.63). It is concluded that algal biomass is as effective as fish oil at enriching broiler diets with C22:6 LC n-3 PUFA, and at equal C22:6n-3 contents, there is no significant difference between these 2 supplements on the oxidative stability of the meat that is produced.

Theory of mind and attentional bias to facial emotional expressions: A preliminary study

Theory of mind ability has been associated with performance in interpersonal interactions and has been found to influence aspects such as emotion recognition, social competence, and social anxiety. Being able to attribute mental states to others requires attention to subtle communication cues such as facial emotional expressions. Decoding and interpreting emotions expressed by the face, especially those with negative valence, are essential skills to successful social interaction. The current study explored the association between theory of mind skills and attentional bias to facial emotional expressions. According to the study hypothesis, individuals with poor theory of mind skills showed preferential attention to negative faces over both non-negative faces and neutral objects. Tentative explanations for the findings are offered emphasizing the potential adaptive role of vigilance for threat as a way of allocating a limited capacity to interpret others’ mental states to obtain as much information as possible about potential danger in the social environment.

Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

The effect of cleft lip on socio-emotional functioning in school-aged children

Background: Children with cleft lip are known to be at raised risk for socio-emotional difficulties, but the nature of these problems and their causes are incompletely understood; longitudinal studies are required that include comprehensive assessment of child functioning, and consideration of developmental mechanisms. Method: Children with cleft lip (with and without cleft palate) (N = 93) and controls (N = 77), previously studied through infancy, were followed up at 7 years, and their socio-emotional functioning assessed using teacher and maternal reports, observations of social interactions, and child social representations (doll play). Direct and moderating effects of infant attachment and current parenting were investigated, as was the role of child communication difficulties and attractiveness. Results: Children with clefts had raised rates of teacher-reported social problems, and anxious and withdrawn-depressed behaviour; direct observations and child representations also revealed difficulties in social relationships. Child communication problems largely accounted for these effects, especially in children with cleft palate as well as cleft lip. Insecure attachment contributed to risk in both index and control groups, and a poorer current parenting environment exacerbated the difficulties of those with clefts. Conclusions: Children with clefts are at raised risk for socio-emotional difficulties in the school years; clinical interventions should focus on communication problems and supporting parenting; specific interventions around the transition to school may be required. More generally, the findings reflect the importance of communication skills for children’s peer relations.

Infant sensitivity to negative maternal emotional shifts: Effects of infant sex, maternal postnatal depression, and interactive style

This study examined the effects of infant sex, maternal postnatal depression, and maternal interactive style on infant sensitivity to maternal negative emotional shifts. Face-to-face interactions of 68 mother–infant dyads were analyzed at 8 and 18 weeks. Twenty-five (28%) mothers had postnatal depression. Interactions were analyzed in terms of overall maternal interactive style: “sensitive,” “anxious,” “intrusive,” and “sad.” Episodes of negative shifts in maternal emotional expression were recorded, along with expressions of infant sensitivity to these changes. Daughters of depressed mothers showed higher rates of sensitivity to maternal negative emotion whereas their sons showed lower rates, in comparison to both girl and boy infants of well mothers. While maternal interactive style had no effect on 8-week infant sensitivity to maternal negative emotional shifts, high rates of 18-week infant sensitivity were predicted by both an 8-week and a concurrent, “sad” maternal interactive style. The findings are discussed in relation to theories of emotional and interpersonal development.

FACSGen: a tool to synthesize emotional facial expressions through systematic manipulation of facial action units

To investigate the perception of emotional facial expressions, researchers rely on shared sets of photos or videos, most often generated by actor portrayals. The drawback of such standardized material is a lack of flexibility and controllability, as it does not allow the systematic parametric manipulation of specific features of facial expressions on the one hand, and of more general properties of the facial identity (age, ethnicity, gender) on the other. To remedy this problem, we developed FACSGen: a novel tool that allows the creation of realistic synthetic 3D facial stimuli, both static and dynamic, based on the Facial Action Coding System. FACSGen provides researchers with total control over facial action units, and corresponding informational cues in 3D synthetic faces. We present four studies validating both the software and the general methodology of systematically generating controlled facial expression patterns for stimulus presentation.

The effect of the year of wheat variety release on productivity and stability of performance on two organic and two non-organic farms

Nineteen wheat cultivars, released from 1934 to 2000, were grown at two organic and two non-organic sites in each of 3 years. Assessments included grain yield, grain protein concentration, protein yield, disease incidence and green leaf area. The superiority of each cultivar (the sum of the squares of the differences between its mean in each environment and the mean of the best cultivar there, divided by twice the number of environments; CS) was calculated for yield, grain protein concentration and protein yield, and ranked in each environment. The yield and grain protein concentration CS were more closely correlated with cultivar release date at the non-organic sites than at organic sites. This difference may be attributed to higher yield levels with larger differences among cultivars at the non-organic sites, rather than to improved stability (i.e. similar ranks) across sites. The significant difference in the correlation of protein yield CS and cultivar age between organic and non-organic sites would support evidence that the ability to take up mineral nitrogen (N) compared to soil N has been a component of the selection conditions of more modern cultivars (released after 1989). This is supported by assessment of green leaf area (GLA), where more modern cultivars in the non-organic systems had greater late-season GLA, a trend that was not identified in organic conditions. This effect could explain the poor correlation between age and protein yield CS in organic compared to non-organic conditions where modern cultivars are selected to benefit from later nitrogen (N) availability which includes the spring nitrogen applications tailored to coincide with peak crop demand. Under organic management, N release is largely based on the breakdown of fertility-building crops incorporated (ploughed-in) in the previous autumn. The release of nutrients from these residues is dependent on the soil conditions, which includes temperature and microbial populations, in addition to the potential leaching effect of high winter rainfall in the UK. In organic cereal crops, early resource capture is a major advantage for maximizing the utilization of nutrients from residue breakdown. It is concluded that selection of cultivars under conditions of high agrochemical inputs selects for cultivars that yield well under maximal conditions in terms of nutrient availability and pest, disease and weed control. The selection conditions for breeding have a tendency to select cultivars which perform relatively better in non-organic compared to organic systems.