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---
title: Q3 2026 Business Review
subtitle: Northwind Technologies · Board quarterly report
author: Business Operations · Finance
date: October 15, 2026
number-sections: true
---

# Key figures {#sec:kpi}

The group booked **USD 68.0 million** in revenue in Q3, up [▲ 18.4%]{color=green .bold} year on year — the **sixth** quarter in a row of double-digit growth. Gross margin reached [32.7%]{color=primary .bold}, a record since the IPO. Operating cash flow exceeded net profit for the first time; [days sales outstanding]{.underline} remain above target and are a priority for Q4[^1].

![Q3 dashboard: (a) monthly revenue by product line and gross margin; (b) revenue mix; (c) growth by region; (d) net profit bridge](images/dashboard.png){#fig:dash width=100%}

<table>
  <caption>Key figures against budget, Q3 2026 {#tbl:kpi}</caption>
  <tr><th rowspan="2">Area</th><th rowspan="2">Measure</th><th colspan="3" align="center">Q3 2026</th><th rowspan="2">y/y</th><th rowspan="2">Status</th></tr>
  <tr><th>Actual</th><th>Budget</th><th>vs budget</th></tr>
  <tr><td rowspan="2"><b>Scale</b></td><td>Revenue (USD m)</td><td align="right"><b>68.0</b></td><td align="right">64.4</td><td align="right">105.7%</td><td align="right"><span style="color:#2E7D32">+18.4%</span></td><td><span style="color:#2E7D32">● Ahead</span></td></tr>
  <tr><td>New contracts (USD m)</td><td align="right"><b>85.7</b></td><td align="right">77.0</td><td align="right">111.3%</td><td align="right"><span style="color:#2E7D32">+26.1%</span></td><td><span style="color:#2E7D32">● Ahead</span></td></tr>
  <tr><td rowspan="2"><b>Profit</b></td><td>Gross margin</td><td align="right"><b>32.7%</b></td><td align="right">31.5%</td><td align="right">+1.2 pt</td><td align="right"><span style="color:#2E7D32">+1.9 pt</span></td><td><span style="color:#2E7D32">● Ahead</span></td></tr>
  <tr><td>Net profit (USD m)</td><td align="right"><b>8.7</b></td><td align="right">8.4</td><td align="right">103.3%</td><td align="right"><span style="color:#2E7D32">+21.6%</span></td><td><span style="color:#2E7D32">● On track</span></td></tr>
  <tr><td rowspan="2"><b>Cash</b></td><td>Operating cash flow (USD m)</td><td align="right"><b>9.9</b></td><td align="right">7.7</td><td align="right">129.1%</td><td align="right"><span style="color:#2E7D32">+48.0%</span></td><td><span style="color:#2E7D32">● Ahead</span></td></tr>
  <tr><td>Days sales outstanding</td><td align="right"><b>96</b></td><td align="right">85</td><td align="right">−11 days</td><td align="right"><span style="color:#C0392B">+7 days</span></td><td><span style="color:#E67E22">▲ Watch</span></td></tr>
</table>

> [!IMPORTANT]
> Cloud now makes up **31.4%** of revenue ([@fig:dash]b) and has become our second growth engine; the West has led regional growth for three quarters running.

# Regions {#sec:region}

<table>
  <caption>Revenue by region and product line (USD m) {#tbl:region}</caption>
  <tr><th rowspan="2">Region</th><th rowspan="2">Market</th><th colspan="2" align="center">Software</th><th colspan="2" align="center">Cloud</th><th rowspan="2">Total</th></tr>
  <tr><th>Q3</th><th>y/y</th><th>Q3</th><th>y/y</th></tr>
  <tr><td rowspan="3"><b>East</b></td><td>New York</td><td align="right">5.9</td><td align="right">+12%</td><td align="right">4.3</td><td align="right"><span style="color:#2E7D32">+41%</span></td><td align="right">12.0</td></tr>
  <tr><td>Boston</td><td align="right">5.3</td><td align="right">+19%</td><td align="right">3.4</td><td align="right"><span style="color:#2E7D32">+36%</span></td><td align="right">9.9</td></tr>
  <tr><td>Philadelphia</td><td align="right">4.6</td><td align="right">+15%</td><td align="right">2.8</td><td align="right">+28%</td><td align="right">8.4</td></tr>
  <tr><td rowspan="2"><b>South</b></td><td>Atlanta</td><td align="right">5.0</td><td align="right">+9%</td><td align="right">3.1</td><td align="right">+24%</td><td align="right">9.2</td></tr>
  <tr><td>Miami</td><td align="right">2.0</td><td align="right">+6%</td><td align="right">1.0</td><td align="right">+18%</td><td align="right">3.4</td></tr>
…

---
title: Attention-Weighted Physics-Informed Neural Networks for the Unsteady Navier–Stokes Equations
author: Ming Wang^1^, Hua Li^1,2^, Siyuan Chen^2^
date: September 2026
abstract: Physics-informed neural networks (PINNs) often fail to converge on unsteady flows at high Reynolds numbers because the gradients of their loss terms are badly out of balance. We propose Attn-PINN, which uses an attention mechanism to weight the residuals adaptively, and prove an upper bound on its approximation error. For flow past a cylinder ($\mathrm{Re}=3\,900$), Attn-PINN reaches a relative $L^2$ error of $1.7\times10^{-3}$ — **an order of magnitude** below the baseline — while training 41% faster.
bibliography: refs.bib
number-sections: true
header-left: Attn-PINN for the Unsteady Navier–Stokes Equations
---

# Introduction

PINNs embed the residual of a partial differential equation in the loss of a neural network [@raissi2019]. They need no mesh and solve forward and inverse problems alike, and have become a core method of scientific machine learning [@karniadakis2021]. For the strongly nonlinear Navier–Stokes equations, however, the gradients of the individual loss terms can differ by more than $10^{3}$, trapping training in a “gradient pathology” [@wang2021]. Neural operators [@li2021] ease the problem but need large amounts of labelled data. Borrowing the attention mechanism of the Transformer [@vaswani2017], we let the network **learn** the weight of every collocation point during training.

# Problem statement {#sec:problem}

Consider incompressible viscous flow in a domain $\Omega\subset\mathbb{R}^2$. The velocity $\mathbf{u}=(u,v)^{\top}$ and pressure $p$ satisfy

$$
\left\{
\begin{aligned}
\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u}
  &= -\frac{1}{\rho}\nabla p + \nu\,\nabla^{2}\mathbf{u} + \mathbf{f},
  && (\mathbf{x},t)\in\Omega\times(0,T],\\
\nabla\cdot\mathbf{u} &= 0,
  && (\mathbf{x},t)\in\Omega\times(0,T],\\
\mathbf{u}(\mathbf{x},0) &= \mathbf{u}_0(\mathbf{x}),
  && \mathbf{x}\in\Omega,
\end{aligned}
\right.
$$ {#eq:ns}

where $\nu$ is the kinematic viscosity. With networks $\hat{\mathbf{u}}_{\theta}$ and $\hat{p}_{\theta}$ approximating the solution, the momentum residual is
$\mathbf{r}_{\theta} = \partial_t\hat{\mathbf{u}}_{\theta} + (\hat{\mathbf{u}}_{\theta}\cdot\nabla)\hat{\mathbf{u}}_{\theta} + \rho^{-1}\nabla\hat{p}_{\theta} - \nu\nabla^{2}\hat{\mathbf{u}}_{\theta} - \mathbf{f}$.

# Method {#sec:method}

## Attention-weighted residuals

For $N_r$ collocation points $\{\mathbf{x}_i\}$, the weights come from scaled dot-product attention over residual features:
…