Organisational Responses to Discontinuous Innovation: A Case Study Approach

Research that examines entrant-incumbent dynamics often points to the organisational limitations that constrain incumbents from successfully pursuing new technologies or fending off new entrants. Some incumbents are nevertheless able to successfully implement organisational structures and develop routines that overcome these institutional constraints. We provide a case-study analysis of how three firms - Motorola, IBM and Kodak - responded to discontinuous innovations and the associated structural and organisational limitations that are typical to incumbent organisations. Each firm was able to capture gains from new technologies and develop profitable products in emerging markets, although their abilities to sustain these gains varied due to subsequent organisational changes. Drawing from these case studies, we synthesise how firms can institute organisational strategies to continue to capture gains from disruptive innovations. A schema suggests that particular organisational strategies are comparatively optimal for corresponding points along an innovation lifecycle

Dilated Floor Functions That Commute

We determine all pairs of real numbers $(\alpha, \beta)$ such that the dilated floor functions $\lfloor \alpha x\rfloor$ and $\lfloor \beta x\rfloor$ commute under composition, i.e., such that $\lfloor \alpha \lfloor \beta x\rfloor\rfloor = \lfloor \beta \lfloor \alpha x\rfloor\rfloor$ holds for all real $x$.Comment: 6 pages, to appear in Amer. Math. Monthl

Dilated floor functions having nonnegative commutator II. Negative dilations

This paper completes the classification of the set $S$ of all real parameter pairs $(\alpha,\beta)$ such that the dilated floor functions $f_\alpha(x) = \lfloor{\alpha x}\rfloor$, $f_\beta(x) = \lfloor{\beta x}\rfloor$ have a nonnegative commutator, i.e. $[ f_{\alpha}, f_{\beta}](x) = \lfloor{\alpha \lfloor{\beta x}\rfloor}\rfloor - \lfloor{\beta \lfloor{\alpha x}\rfloor}\rfloor \geq 0$ for all real $x$. This paper treats the case where both dilation parameters $\alpha, \beta$ are negative. This result is equivalent to classifying all positive $\alpha, \beta$ satisfying $\lfloor{\alpha \lceil{\beta x}\rceil}\rfloor - \lfloor{\beta \lceil{\alpha x}\rceil}\rfloor \geq 0$ for all real $x$. The classification analysis is connected with the theory of Beatty sequences and with the Diophantine Frobenius problem in two generators.Comment: 18 pages, 8 figure

The family of aa-floor quotient partial orders

An approximate divisor order is a partial order on the positive integers $\mathbb{N}^+$ that refines the divisor order and is refined by the additive total order. A previous paper studied such a partial order on $\mathbb{N}^+$, produced using the floor function. A positive integer $d$ is a floor quotient of $n$, denoted $d \,\preccurlyeq_{1}\, n$, if there is a positive integer $k$ such that $d = \lfloor{n / k}\rfloor$. The floor quotient relation defines a partial order on the positive integers. This paper studies a family of partial orders, the $a$-floor quotient relations $\,\preccurlyeq_{a}\,$, for $a \in \mathbb{N}^+$, which interpolate between the floor quotient order and the divisor order on $\mathbb{N}^+$. The paper studies the internal structure of these orders.Comment: 30 pages, 3 figures, comments welcome! arXiv admin note: text overlap with arXiv:2212.1168

Radiative And Electroweak Penguin Decays of B

Radiative and electroweak penguin decays of B mesons are flavor-changing-neutral-current processes that provide powerful ways to test the Standard Model at the one-loop level, to search for the effects of new physics, and to extract Standard Model parameters such as CKM matrix elements and quark masses. The large data samples obtained by the B-factory experiments BaBar and Belle, together with an intensive theoretical effort, have led to significant progress towards understanding these rare decays. Recent experimental results include the measurements of the b {yields} d{gamma} decays B {yields} {rho}({omega}){gamma}, the observation of B {yields} K(*){ell}{sup +}{ell}{sup -} decays (together with studies of the associated kinematic distributions), and improved measurements of the inclusive B {yields} Xs{gamma} rate and photon energy spectrum

Independent evaluation of a simple clinical prediction rule to identify right ventricular dysfunction in patients with shortness of breath

BACKGROUND: Many patients have unexplained persistent dyspnea after negative computed tomographic pulmonary angiography (CTPA). We hypothesized that many of these patients have isolated right ventricular (RV) dysfunction from treatable causes. We previously derived a clinical decision rule (CDR) for predicting RV dysfunction consisting of persistent dyspnea and normal CTPA, finding that 53% of CDR-positive patients had isolated RV dysfunction. Our goal is to validate this previously derived CDR by measuring the prevalence of RV dysfunction and outcomes in dyspneic emergency department patients. METHODS: A secondary analysis of a prospective observational multicenter study that enrolled patients presenting with suspected PE was performed. We included patients with persistent dyspnea, a nonsignificant CTPA, and formal echo performed. Right ventricular dysfunction was defined as RV hypokinesis and/or dilation with or without moderate to severe tricuspid regurgitation. RESULTS: A total of 7940 patients were enrolled. Two thousand six hundred sixteen patients were analyzed after excluding patients without persistent dyspnea and those with a significant finding on CTPA. One hundred ninety eight patients had echocardiography performed as standard care. Of those, 19% (95% confidence interval [CI], 14%-25%) and 33% (95% CI, 25%-42%) exhibited RV dysfunction and isolated RV dysfunction, respectively. Patients with isolated RV dysfunction or overload were more likely than those without RV dysfunction to have a return visit to the emergency department within 45 days for the same complaint (39% vs 18%; 95% CI of the difference, 4%-38%). CONCLUSION: This simple clinical prediction rule predicted a 33% prevalence of isolated RV dysfunction or overload. Patients with isolated RV dysfunction had higher recidivism rates and a trend toward worse outcomes

Hyperactivity, impulsivity, and inattention in boys with cleft lip and palate: relationship to ventromedial prefrontal cortex morphology

The purpose of this study is to evaluate quantitative structural measures of the ventromedial prefrontal cortex (vmPFC) in boys with isolated clefts of the lip and/or palate (ICLP) relative to a comparison group and to associate measures of brain structure with quantitative measures of hyperactivity, impulsivity, and inattentiveness. A total of 50 boys with ICLP were compared to 60 healthy boys without clefts. Magnetic resonance imaging brain scans were used to evaluate vmPFC structure. Parents and teachers provided quantitative measures of hyperactivity, impulsivity, and inattentiveness using the Pediatric Behavior Scale. Boys with ICLP had significantly higher ratings of hyperactivity/impulsivity/inattention (HII) and significantly increased volume of the right vmPFC relative to the comparison group. There was a direct relationship between HII score and vmPFC volume in both the ICLP group and control group, but the relationship was in the opposite direction: in ICLP, the higher the vmPFC volume, the higher the HII score; for the comparison group, the lower the vmPFC volume, the greater the HII score. The vmPFC is a region of the brain that governs behaviors of hyperactivity, impulsivity and inattention (HII). In boys with ICLP, there are higher levels of HII compared to the controls and this is directly related to a significantly enlarged volume of the right vmPFC. Enlargement of this region of the brain is therefore considered to be pathological in the ICLP group and supports the notion that abnormal brain structure (from abnormal brain development) is the underlying etiology for the abnormal behaviors seen in this population